STUART KYLE DUNCAN, Circuit Judge

Thomas Miles Farrell, Attorney, Charles Bedford Hampton, Esq., McGuireWoods, L.L.P., Houston, TX, Emil Lippe, Jr., Lippe & Associates, Dallas, TX, for Plaintiff-Appellant.

Tom Moore Dees, III, Esq., Stewart Hyer Thomas, Attorneys, Hallett & Perrin, P.C., Dallas, TX, for Defendant-Appellees Heather V. Washburne and Elisa M. Summers.

W. Scott Hastings, Esq., Locke Lord, L.L.P., Dallas, TX, David J. Beck, Esq., Beck Redden, L.L.P., Houston, TX, Quentin Brogdon, Crain Lewis Brogdon, L.L.P., Dallas, TX, Murray Jules Fogler, Esq., Attorney, Fogler Brar O'Neil & Gray, L.L.P., Houston, TX, Carrie L. Huff, Esq., Haynes & Boone, L.L.P., Dallas, TX, Gilbert I. Low, Orgain, Bell & Tucker, L.L.P., Beaumont, TX, Brian E. Mason, Dorsey & Whitney, L.L.P., Dallas, TX, Eric Thomas Stahl, Law Offices of Frank L. Branson, P. C., Dallas, TX, for Defendant-Appellee Margaret Keliher.

Before OWEN, Chief Judge, and BARKSDALE and DUNCAN, Circuit Judges.

STUART KYLE DUNCAN, Circuit Judge:

Once again, we consider a dispute related to trusts formed by Haroldson Lafayette ("H.L.") Hunt, the late Texas oil baron reputed to be one of the world’s richest men when he died in 1974. See generally Hill v. Schilling , 495 F. App'x 480, 482 (5th Cir. 2012) (describing formation of the trusts); Hill v. Hunt , 2009 WL 5125085, at *1 (N.D. Tex. Dec. 29, 2009) (same). After "protracted [and] complicated" litigation, Hill v. Schilling , 593 F. App'x 330, 331 (5th Cir. 2014), squabbling over the trusts was supposedly ended by a settlement agreement confected in 2010. Yet, over the next four years, our court "weighed in on the settlement" four times. Id. This appeal makes it five.

The latest chapter concerns part of the settlement in which Hunt’s grandson, plaintiff-appellant Albert G. Hill III ("Hill III"), promised—in exchange for a nine-figure payment—not to contest the last will and testament of his father, Albert Hill, Jr. ("Hill Jr."). When Hill Jr. died, however, Hill III challenged the will in Texas probate court, lost, and appealed. In turn, Hill III’s sisters (Heather Washburne and Elisa Summers), defendant-appellees here, asked the federal district court to enforce the settlement agreement and enjoin Hill III’s will challenges, including those in the ongoing probate court proceedings and appeal. The district court agreed, granting an injunction that, among other things, ordered Hill III to withdraw his state appeal. Hill III now appeals the injunction.

We hold that Hill III’s appeal of the injunction is, in most respects, moot. That is because, in the interim, the Texas appeals court has lost jurisdiction over Hill III’s state appeal and Hill III has withdrawn his failed will challenges in the probate court. The terms of the injunction related to those probate proceedings have thus been irrevocably fulfilled and nothing we might say about those provisions would afford Hill III any relief. His appeal is not moot, however, as to the terms in the injunction that prohibit Hill III from challenging his father’s will ever again, in any court. As to those terms, Hill III’s challenges all fail. We therefore dismiss in part and affirm in part. We also remand to allow the district court to consider whether the sisters are entitled to additional costs and fees.

I.

A.

In 2007, Hill III sued his sisters and Hill Jr. in state court. The lawsuit alleged misadministration of two trusts of which Hill III was a beneficiary. The suit was removed by consent and ultimately settled in May 2010, along with many other lawsuits concerning the Hill and Hunt families’ estates.

At issue now is the settlement agreement. See Hill , 495 F. App'x at 482–83 (discussing genesis of settlement agreement). In exchange for a nine-figure payment and other benefits, Hill III agreed "not to contest the Last Will and Testament of Al Jr. or file any additional action, lawsuit, or legal proceeding challenging the disposition of his property" (the no-contest clause). The parties further "agree[d] that the remedy of specific performance and/or injunctive relief (whether mandatory or by restraint) shall be available for the breach of any term, condition, covenant, or warranty of" the settlement agreement. The parties consented to the district court’s continuing jurisdiction over actions to enforce the settlement agreement.

In November 2010, the district court approved the settlement agreement and entered final judgment. The judgment incorporated the settlement agreement by reference and reproduced the no-contest clause in virtually identical language, ordering Hill III not to "contest the Last Will and Testament of Al Jr., or file any additional action, lawsuit, or legal proceeding challenging the disposition of Al Jr.’s property."

Despite having executed the settlement agreement that served as its basis, Hill III appealed the final judgment, challenging, among other things, its implementation of the settlement agreement on grounds not at issue here. See id. at 483, 484–85. A panel of our court affirmed. Id. at 488. Thereafter, Hill III challenged the final judgment yet again, resurrecting a previously rejected claim that the district judge should have recused himself because of a financial interest of his wife. Hill , 593 F. App'x at 332. A panel of our court again affirmed. Id. at 335.

B.

Hill Jr. died on December 2, 2017. Two versions of Hill Jr.’s putative will were produced in probate court, and while their provisions are identical, Hill III argues that "the signatures and initials on them are very different, raising serious questions about whether either version was actually signed by Al Jr." Both documents were dated December 20, 2014, and, consistent with the settlement agreement, both excluded Hill III from any benefit.

On December 22, 2017, Hill III entered the probate proceedings, challenging terms of the will that appointed executors to a number of trusts. Those challenges are not at issue here.

On May 29, 2018, Hill III’s sisters asked the district court to enjoin Hill III’s claims in probate court on the ground that they violated the no-contest clause. Hill responded with his own motion to enforce the settlement agreement and final judgment. On July 3, 2018, the district court denied all relief without prejudice, holding any relief would be "premature" because of the pending probate proceedings.

On July 13 and August 3, 2018, Hill III filed amended answers in the probate court, in which he argued that the putative will had not actually been executed by Hill Jr.; that Hill Jr. lacked capacity when the will was executed; and that Hill Jr. had subsequently revoked the putative will. Hill III also challenged the putative will’s choice of independent executor. His sisters objected to these challenges in probate court, arguing they violated the settlement agreement and final judgment. The probate court noted the objection and continued the trial.

The sisters returned to the district court, renewing their request for injunctive relief only as to the challenges to Hill Jr.’s will in the amended answers (the "will challenges"). The district court deferred ruling, as Hill III had not filed a response and the probate court had not yet ruled on the sisters’ similar objection. A few days later, the probate court sustained the sisters’ objection and held that the settlement agreement and final judgment barred the will challenges. Hill III appealed the decision to the Texas court of appeals.

C.

In light of Hill III’s appeal of the probate court’s decision, his sisters renewed in the district court their requests for injunctive relief, costs, and attorneys’ fees. The matter was fully briefed.

The district court granted the sisters an injunction on December 7, 2018. It rejected Hill III’s argument that the Anti-Injunction Act barred the injunction, holding that the injunction was "necessary in aid of [the district court’s] jurisdiction" and "to protect and effectuate" the final judgment. See 28 U.S.C. § 2283. The district court also noted several previous occasions on which Hill III had violated the final judgment and thus held that the injunction was authorized by the All Writs Act, 28 U.S.C. § 1651(a), in order to "deter and prevent future litigation of previously decided issues by a vexatious litigant."

Next, the district court held that Hill III’s claims in probate court violated the no-contest clause. It applied Texas contract law to the clause and concluded its meaning was unambiguous. It then cited several Texas cases holding that challenges to testamentary capacity, execution, and executor appointment constitute "will contests." See , e.g. , Gunter v. Pogue , 672 S.W.2d 840, 841–43 (Tex. App.—Corpus Christi 1984, writ ref’d n.r.e.) (testamentary incapacity and undue influence claims were "unquestionably a will contest"); Short v. Short , 468 S.W.2d 164, 165 (Tex. Civ. App.—Tyler 1971, writ ref’d n.r.e.) (attacking genuineness of signature on will was "a will contest"). The court further agreed with the sisters that principles of quasi-estoppel rendered Hill III’s challenges "inequitable."

Finally, the district court found that the remaining permanent-injunction elements were met. See , e.g. , VRC LLC v. City of Dallas , 460 F.3d 607, 611 (5th Cir. 2006) (reciting elements). It found that but for the injunction, the sisters would suffer irreparable harm because they would "not have received the benefit of their bargain under the [no-contest clause]." Balancing the potential harms to Hill III and the sisters, the district court found "it would be unconscionable to allow" Hill III to appeal the probate court’s order. Finally, enforcing the final judgment and settlement agreement would "not disserve the public interest because movants are asking the court to enforce the parties" own agreements.

The resultant injunction prohibited Hill III and his attorneys "from violating the Final Judgment or breaching the Settlement Agreement" by appealing the probate court’s order or contesting Hill Jr.’s will "in any manner," including through the challenges Hill III brought below. The injunction also ordered Hill III and his attorneys to "dismiss or withdraw" the will challenges "and any appeal taken therefrom." The court awarded the sisters costs and fees.

On December 20, 2018, Hill III timely appealed to this court the order granting the injunction. He also sought stays from the district court and this court, arguing that "absent a stay," he would "lose his rights to appeal the probate court orders" because "the state appellate court will forever lose jurisdiction to review the Probate Court’s order." Both stays were denied.

Hill III then moved to dismiss his state appeal "under protest" and "reserv[ing] the right to move in [the Texas court of appeals] to reinstate the appeal" should this panel rule in his favor. The Texas court of appeals dismissed the matter on January 24, 2019, noting: "In the motion, appellant states ‘he reserves the right’ to move to reinstate this appeal should a certain circumstance arise. Any such motion must be filed in accordance with Texas Rule of Appellate Procedure 49," which authorizes motions for rehearing. The mandate issued on April 8, 2019. Hill III also withdrew the will challenges from the probate court.

II.

"The decision to grant or deny permanent injunctive relief is an act of equitable discretion by the district court, reviewable on appeal for abuse of discretion." eBay Inc. v. MercExchange, L.L.C. , 547 U.S. 388, 391, 126 S.Ct. 1837, 164 L.Ed.2d 641 (2006) (citation omitted). The district court’s findings of fact and all its determinations regarding the equitable injunction factors are reviewed for clear error. Peaches Entm’t Corp. v. Entm’t Repertoire Assocs., Inc. , 62 F.3d 690, 693 (5th Cir. 1995). Its conclusions of law are reviewed de novo . Id.

III.

A.

We first consider whether Hill III’s appeal of the injunction is moot and, if it is, what remedy should follow.

1.

Hill III’s sisters claim his appeal of the injunction is moot because the Texas court of appeals has lost jurisdiction over his appeal of the probate court’s order. We agree as to the provisions of the injunction barring Hill III’s appeal of the probate court order and requiring him to withdraw his probate court claims. Those provisions have already been fulfilled, and so, as to them, Hill III’s appeal is moot.

"An actual case or controversy must exist at every stage in the judicial process." Motient Corp. v. Dondero , 529 F.3d 532, 537 (5th Cir. 2008) (citation omitted). Therefore, we must dispose of an appeal if "an event occurs while a case is pending on appeal that makes it impossible for the court to grant any effectual relief whatever to a prevailing party." Id. (quoting Church of Scientology v. United States , 506 U.S. 9, 12, 113 S.Ct. 447, 121 L.Ed.2d 313 (1992) ). The appeal of an injunction is moot if its terms have been executed "fully and irrevocably." Univ. of Tex. v. Camenisch , 451 U.S. 390, 398, 101 S.Ct. 1830, 68 L.Ed.2d 175 (1981) ; see also, e.g. , Seattle-First Nat’l Bank v. Manges , 900 F.2d 795, 798 (5th Cir. 1990) (appeal moot when appellant had complied with "discrete, mandatory order" to transfer venue).

The injunction permanently prohibits Hill III "from violating the Final Judgment or breaching the Settlement Agreement" by taking any of three actions: (1) by contesting Hill Jr.’s will "in any matter ... in the Probate Court or in any other court"; (2) by appealing the probate court’s order regarding the settlement agreement; and (3) by appealing the probate court’s admission of the will. It further affirmatively obliges Hill III and his attorneys to dismiss or withdraw his claims in probate court, including through appeal. Finally, it prohibits Hill III’s attorneys from "filing, pursuing, or prosecuting any action ... that violates the terms of the Settlement Agreement or Final Judgment."

Hill III’s appeal is moot as to the injunction’s prohibitions on appealing the probate court’s order and appealing the probate court’s admission of the will, and also as to its command to dismiss or withdraw his probate court claims, including through appeal. These terms have been executed fully and irrevocably. This is because the Texas court of appeals has lost jurisdiction over Hill III’s appeal of the probate court’s order, such that the order will stand regardless of our decision.

Texas courts of appeals have jurisdiction to "vacate or modify [their] judgment[s]" only through their so-called "plenary power." Tex. R. App. P. 19.3. The Texas Rules of Appellate Procedure provide that the plenary power expires either "60 days after judgment if no timely filed motion for rehearing or en banc reconsideration, or timely filed motion to extend time to file such a motion, is then pending" or "30 days after the court overrules all timely filed motions for rehearing or en banc reconsideration, and all timely filed motions to extend time to file such a motion." Tex. R. App. P. 19.1. After the expiration of time under Rule 19.1, the court lacks jurisdiction to "vacate or modify [its] judgment." Kacal v. Cohen , 13 S.W.3d 900, 902 (Tex. App.—Waco 2000, no pet.) (citation omitted).

Here, the Texas court of appeals issued its judgment dismissing Hill III’s appeal on January 24, 2019. Hill III had until March 25, 2019, to move for rehearing, for en banc reconsideration, or to extend time to move for either form of relief. He filed no such motions. The court of appeals therefore lacks jurisdiction over his appeal. Accordingly, Hill III has "fully and irrevocably" executed the injunction’s prohibitions on appealing the probate court’s order and the probate court’s admission of the will, as well as its command to dismiss or withdraw his probate court claims, including through appeal. Camenisch , 451 U.S. at 398, 101 S.Ct. 1830. It is therefore "impossible" for us "to grant any effectual relief whatever" to Hill III as to these provisions. Dondero , 529 F.3d at 537.

This conclusion is supported by Humble Exploration Co. v. Browning , in which a Texas court of appeals refused to reinstate an out-of-time appeal, even after our court reversed a district court’s order holding that the underlying state proceedings were void. 690 S.W.2d 321, 329 (Tex. App.—Dallas 1985, writ ref’d n.r.e.). Even though the Texas court of appeals still retained plenary power over its previous judgment, id. at 327, it refused to revisit it, reading the relevant filing deadline as "a strict limitation upon the authority of the courts of appeals to consider and grant untimely motions for rehearing." Id. at 325. This was the case regardless of our court’s decision, which Chief Justice Guittard noted in dissent "completely undermine[d]" the merits of the decision the Texas court of appeals was being asked to reconsider. Id. at 330 (Guittard, C.J., dissenting).

Hill III claims his sisters "misinterpret" Browning because while it refused to reinstate the appeal, it also held "that the court of appeals does possess a plenary power over its judgments within the term after the motion for rehearing is overruled." 690 S.W.2d at 322. This was true at the time Browning was decided but is no longer the case, as Rule 19.1, which took effect twelve years after Browning , now defines the time limit of the plenary power. See Kacal , 13 S.W.3d at 902. And, in any event, Browning denied rehearing despite having plenary power over the appeal.

If anything, Hill III’s case in the state court of appeals would be weaker than the defendant-appellees’ in Browning . Against him is not only Texas’s strict adherence to filing deadlines but the fact that Rule 19.1 now limits the court’s plenary power. In Browning , all that could have saved the defendant-appellees was the court’s plenary power—it was undisputed that the plenary power was available to the court as long as it vacated the order within the same term. The relevant disagreement was over whether to use the plenary power that no one doubted existed. See 690 S.W.2d at 325–27. Here, in contrast, the court has no such plenary power. See Tex. R. App. P. 19.1(a). Hill III’s other arguments fare no better. Hill III argues that he did "everything possible" to preserve his rights without violating the injunction. He claims that appealing to the Supreme Court of Texas or seeking rehearing would have violated the injunction, which ordered him "to ‘dismiss’ his appeal." "After all," he claims, "any of these actions would have required [him] to argue that his appeal should not, in fact, be dismissed, running afoul of the District Court’s broad injunction that [he] ‘dismiss’ the appeal."

Hill III gives no reason to think this claimed catch-22 would affect the state court of appeals’ jurisdiction, and Browning strongly suggests it would not. Regardless, Hill III ignores the most logical option he had in state court: moving to extend time to file a motion for rehearing. See Tex. R. App. P. 19.1(a) (plenary power expires "60 days after judgment if no timely filed motion for rehearing or en banc reconsideration, or timely filed motion to extend time to file such a motion , is then pending" (emphasis added)). Hill III answers only that "ask[ing] the Texas Court of Appeals to ... indefinitely delay his dismissal ... would have required [him] to argue that his appeal should not , in fact, be dismissed." But he does not explain how asking for an extension of time would require him to argue the merits of his appeal or how doing so would violate the injunction.

Hill III also argues we or the district court could give him effective relief by "ask[ing]" the probate court to "issue a new order," thereby giving him another opportunity to appeal. He cites no legal authority, however, suggesting that we or the district court have power to order the probate court to reconsider its order. He similarly does not explain how such an order from us or the district court would not be an extrajurisdictional "collateral attack[ ] on" the probate court’s proceedings. Bell v. Valdez , 207 F.3d 657 (5th Cir. 2000) ("Under the Rooker-Feldman doctrine, federal courts lack jurisdiction to entertain" such attacks. (citation omitted)).

This appeal is therefore moot as to the injunction’s prohibitions on appealing the probate court’s order and appealing the probate court’s admission of the Will, and as to its command to dismiss or withdraw Hill III’s probate court challenges, including through appeal.

2.

Even though neither party briefs the question, we must decide what effect flows from the mootness of Hill III’s appeal.

"Our disposition of a moot case may depend on when mootness occurred." Goldin v. Bartholow , 166 F.3d 710, 718 (5th Cir. 1999). If the case became moot before the injunction was issued, we must vacate with instructions to dismiss the case. Id. This is because, like us, "[t]he district court has no power to decide moot causes." Id. (citation omitted). If, on the other hand, the case became moot after the district court’s decision, whether we should vacate the order—or instead simply dismiss the appeal, allowing the order to stand—depends on whether "the mootness can be traced to the actions of the party seeking vacatur ." Id. at 719 (citation omitted); see also, e.g. , Staley v. Harris Cty. , 485 F.3d 305, 311 n.2 (5th Cir. 2007) (en banc) (collecting decisions and explaining that "in cases mooted by the voluntary actions or inactions of a party, we have decided the vacatur question in favor of the party that did not cause the case to become moot"). This doctrine, established in United States v. Munsingwear , 340 U.S. 36, 71 S.Ct. 104, 95 L.Ed. 36 (1950), is "an equitable one, justified as a means of avoiding the unfairness of a party’s being denied the power to appeal an unfavorable judgment by factors beyond its control." Goldin , 166 F.3d at 719 (citation omitted); accord U.S. Bancorp Mortg. Co. v. Bonner Mall P’ship , 513 U.S. 18, 24, 115 S.Ct. 386, 130 L.Ed.2d 233 (1994) ("From the beginning" of the Munsingwear doctrine, "we have disposed of moot cases in the manner most consonant to justice, in view of the nature and character of the conditions which have caused the case to become moot." (citation omitted; cleaned up)).

Here, the injunction was entered on December 7, 2018, and the case became moot on March 25, 2019, Hill III’s deadline to seek an extension to request rehearing in the Texas court of appeals. Whether the now-moot terms of the injunction should be vacated, then, depends on whether mootness can be traced to Hill III’s actions. See Goldin , 166 F.3d at 719. We conclude that it can: Hill III caused the appeal’s mootness by failing to seek an extension to request rehearing. The alternative, vacating the district court’s injunction, would unjustly reward Hill III for sitting on his rights.

We therefore decline to vacate the injunction’s already-fulfilled terms. Instead, we will dismiss the appeal as to those terms.

B.

The injunction is not moot in all respects, however. In addition to the already-fulfilled terms, the injunction also enjoins Hill III "from violating the Final Judgment or breaching the Settlement Agreement" by, inter alia , contesting Hill Jr.’s will "in any manner ... in the Probate Court or in any other court." It further prohibits Hill III’s attorneys from "filing, pursuing, or prosecuting any action ... that violates the terms of the Settlement Agreement or Final Judgment." As the sisters conceded at oral argument, the appeal is not moot as to these future-looking provisions. Hill III has not fulfilled these terms because they apply permanently, and he could violate them at any time.

We must therefore address the rest of Hill III’s challenges as applied to these future-looking terms. These challenges all fail.

1.

Hill III argues that the injunction violates the Anti-Injunction Act ("AIA"), which provides that "[a] court of the United States may not grant an injunction to stay proceedings in a State court except as expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments." 28 U.S.C. § 2283.

The district court held that the injunction was necessary "to protect or effectuate" the final judgment. This provision is sometimes called the "relitigation exception" to the AIA because it allows federal courts to stay state-court proceedings in order to prevent a party from relitigating in state court issues that "have been decided by the federal court." Chick Kam Choo v. Exxon Corp. , 486 U.S. 140, 147–48, 108 S.Ct. 1684, 100 L.Ed.2d 127 (1988).

In the alternative, the district court held that the injunction was "necessary in aid of its jurisdiction." And finally, noting Hill III’s "well-documented history of ignoring his contractual obligations under the Settlement Agreement"—including by failing to appraise certain illiquid trust assets and by using $9 million held in trust for Hill Jr.’s grandchildren "to support his and [his wife’s] lavish lifestyle" —the district court held that the injunction was authorized by the All Writs Act, 28 U.S.C. § 1651(a), as a "narrowly tailored order[ ] enjoining repeatedly vexatious litigants from filing future state court actions." Newby v. Enron Corp. , 302 F.3d 295, 301 (5th Cir. 2002) (citation omitted).

We need not decide whether any of these exceptions applies because the only non-moot challenges to the injunction concern its forward-looking terms, which do not stay any ongoing state-court proceedings. See 28 U.S.C. § 2283 (absent specific exceptions, prohibiting federal courts from "grant[ing] an injunction to stay proceedings in a State court"); see also Dombrowski v. Pfister , 380 U.S. 479, 485 n.2, 85 S.Ct. 1116, 14 L.Ed.2d 22 (1965) ( § 2283 bars only "stays of suits already instituted" but does not "preclude injunctions against the institution of state court proceedings" (citation omitted)). Hill III offers no argument otherwise.

Even if this were not the case, we agree with the district court that the injunction falls squarely under the relitigation exception. The injunction is "necessary to protect" and "effectuate" the final judgment, 28 U.S.C. § 2283, which prohibits Hill III from contesting the will in state (as well as federal) court. Hill III’s only argument to the contrary—that "the issue being litigated in Texas state court—whether the Alleged Will was [Hill] Jr.’s valid last will and testament—has not been previously litigated in the District Court or elsewhere"—is a red herring. It is true that for the relitigation exception to apply, the enjoined litigation must involve an issue "actually" decided by the federal court. Chick Kam Choo , 486 U.S. at 148, 108 S.Ct. 1684. But here, both the district court and the probate court did decide that the no-contest clause bars Hill III’s challenges in probate court. The district court enjoined Hill III from relitigating that decision by appealing the probate court’s order. The merits of the will challenges were immaterial to both the state and federal orders.

2.

Hill III also claims the will challenges fall outside the scope of the no-contest clause, arguing the district court misinterpreted the clause by assuming that the putative will is in reality the "Last Will and Testament of Al Jr." Hill III claims there is "substantial reason" to doubt the putative will’s validity.

As with the AIA, we need not resolve this argument because Hill III’s appeal is moot as to the terms of the injunction that bar the particular will challenges he claims are outside the no-contest clause’s scope. Nonetheless, we note our agreement with the district court that Hill III’s reading of the no-contest clause is flawed. Nowhere in his briefing does Hill III describe what challenges the no-contest clause would bar. Contracts should be interpreted to "give effect to all the provisions of the contract so that none will be rendered meaningless." Italian Cowboy Partners, Ltd. v. Prudential Ins. Co. of Am. , 341 S.W.3d 323, 333 (Tex. 2011) (citation omitted).

3.

Next, Hill III challenges the district court’s findings on the equitable injunction factors, which we review for clear error. Peaches Entm’t Corp. , 62 F.3d at 693. In addition to succeeding on the merits, a party seeking an injunction must show that (1) "the failure to grant the injunction will result in irreparable injury," (2) that injury "outweighs any damage that the injunction will cause the opposing party," and (3) "the injunction will not disserve the public interest." United Motorcoach Ass’n, Inc. v. City of Austin , 851 F.3d 489, 492–93 (5th Cir. 2017) (citation omitted). The district court did not clearly err as to any of these factors.

First, the district court held that, but for the injunction, Hill III’s sisters would suffer irreparable harm not only by having to defend against the state appeal but also by being deprived irreparably of the benefit of their bargain under the settlement agreement. The district court relied on the settlement agreement’s provision recognizing that injunctive relief would be appropriate and on Hill III’s history of ignoring court orders and flouting the agreement. On appeal, Hill III cites Renegotiation Board v. Bannercraft Clothing Co., Inc. for the proposition that "[m]ere litigation expense, even substantial and unrecoupable cost, does not constitute irreparable injury." 415 U.S. 1, 24, 94 S.Ct. 1028, 39 L.Ed.2d 123 (1974) (citations omitted). This misses the mark: the expense at issue in Bannercraft was the expense of litigating the instant case, not a parallel proceeding in another court. Id. Here, the sisters’ irreparable harm was not the expense of defending this appeal ; it was the expense of defending against Hill III’s challenges in the probate court, depriving them of the benefit of their bargain under the settlement agreement.

Second, the district court determined that the balance of equities favored an injunction: without it, the sisters would have to continue defending the state litigation, whereas Hill III—having agreed to the no-contest clause—had no right to proceed in that litigation. On appeal, Hill III argues that he suffered irreparable injury because the injunction required him to forego his right to appeal the probate court’s order. We disagree. As discussed above, Hill III ignores that he could have simply asked the Texas court of appeals for an extension of time in which to ask for reconsideration. And regardless, Hill III relinquished his right to appeal the order in the no-contest clause.

Third, the public interest favors enforcing the no-contest provision according to its terms. The sisters correctly note that Texas favors the validity and enforcement of settlement agreements. See Tex. Civ. Prac. & Rem. Code § 154.002. More importantly, public interest favors disallowing vexatious litigation. See , e.g. , Harrelson v. United States , 613 F.2d 114 (5th Cir. 1980) (observing that "[a] litigious plaintiff pressing a frivolous claim ... can be extremely costly to the defendant and can waste an inordinate amount of court time").

4.

Finally, Hill III claims the injunction violates Federal Rule of Civil Procedure 65(d)(1), which provides that an injunction must "describe in reasonable detail—and not by referring to the complaint or other document—the act or acts restrained or required." The injunction provides that Hill III is prohibited from "violating the Final Judgment or breaching the Settlement Agreement by" committing certain acts, including contesting Hill Jr.’s will "in any manner." The injunction also describes in detail what actions Hill III and his lawyers must take to dismiss the appeal and withdraw the will contest.

While the injunction does "refer[ ] to" the settlement agreement and final judgment, it does not rely on either document to describe its requirements. That is, the injunction does not prohibit Hill III from violating the final judgment or the settlement agreement as such. Instead, it prohibits Hill III from violating those documents by taking certain, specific actions. The injunction therefore did not "engraft" the final judgment or settlement agreement "in gross" or "rely on" either document "for clarification of what was otherwise unclear in the decree itself." Scott v. Schedler , 826 F.3d 207, 213 (5th Cir. 2016) (quoting Gulf King Shrimp Co. v. Wirtz , 407 F.2d 508, 517 (5th Cir. 1969) ) (cleaned up). Instead, "[i]t merely supplemented specific instructions in the decree with the ... authority from which the right to issue such instructions derived." Id. (citation omitted; cleaned up).

The injunction therefore does not violate Rule 65.

* * *

We therefore DISMISS the appeal as to the following, already-fulfilled terms of the injunction: its prohibition on contesting Hill Jr.’s will in the current probate proceedings; its prohibition on appealing the probate court’s order regarding the settlement agreement; its prohibition on appealing the probate court’s admission of the will; and its obligation to dismiss or withdraw his claims in probate court, including through appeal.

We AFFIRM the rest of the order, including the following, future-looking terms of the injunction: its prohibition on contesting Hill Jr.’s will "in any manner," in any court; and its prohibition on "filing, pursuing, or prosecuting any action ... that violates the terms of the Settlement Agreement or Final Judgment."

Finally, we REMAND to the district court for the limited purpose of addressing whether the sisters are entitled to additional costs and fees. Cf. Instone Travel Tech Marine & Offshore v. Int’l Shipping Partners, Inc. , 334 F.3d 423, 433 (5th Cir. 2003) (remanding "to allow the district court to make the initial determination and award of appellate attorney’s fees").

DISMISSED in part; AFFIRMED in part; and REMANDED for further proceedings.