Judges are used to deciding disputes, and Supreme Court justices especially are accustomed to having the last word.

So an attorney for the Scottish mother at the heart of an international child-custody case was gentle in telling the justices on Wednesday that the services of the U.S. courts are no longer required.

“It’s an answer that justices and judges typically don’t want to hear,” Washington lawyer Stephen J. Cullen said. “But it is the answer. . . . There is nothing left to be done.”

Some justices considering the case did not seem quite so resigned.

The question is whether Army Sgt. 1st Class Jeffrey Lee Chafin can appeal a federal judge’s decision to let his estranged wife, Lynne Hales Chafin, take their daughter, Eris, to her native country. The U.S. Court of Appeals for the 11th Circuit in Atlanta said that the case was moot because the girl was lawfully taken to Scotland and that all custody proceedings must now take place there.

Chief Justice John G. Roberts Jr. said that would be an incentive for a parent who wins the right to remove a child to another country to “leave immediately,” before there is a chance to appeal the decision.

“Get on the first plane out, and then you’re home free,” Roberts said. “That seems to me to be a very unfortunate result.”

The justices were considering the role of courts in interpreting the Hague Convention on the Civil Aspects of International Child Abduction, to which the United States is one of more than 80 signatories.

The treaty mandates that if a parent takes a child from one country to another, the other parent may file a petition asking that the child be returned. If the petition is granted, any custody claims must be heard in the country of “habitual residence.”

“The whole object of the Hague Convention is to stop this shuttling the child back and forth,” Justice Ruth Bader Ginsburg told a government lawyer who agreed with Jeffrey Chafin that his appeal should be heard even though his daughter is in Scotland.

“What you’re urging is exactly what this convention was meant to stop.”

But the treaty is silent on what happens when the losing parent wants to appeal a court’s initial decision on “habitual residency.” It is an especially important issue for military families such as the Chafins, the government said.

The couple were married in Scotland in 2006, and their daughter was born the next year. They lived together in Germany until he was deployed to Afghanistan, and mother and daughter moved to Scotland.

Jeffrey Chafin was transferred to Alabama in 2009 and, even though the marriage was in trouble, the family reunited there. They agreed to divorce in 2010, Lynne Chafin was deported after her visa expired, and then she filed her petition to have Eris join her in Scotland.

A federal judge in Alabama agreed with Lynne Chafin and declined to grant a stay of the order. Mother and child departed that day. When Jeffrey Chafin appealed the order, the 11th Circuit dismissed his petition because it said that there was nothing left for U.S. courts to decide.

Chafin has since filed for custody of his daughter in Scotland.

But his attorney, Michael E. Manely of Marietta, Ga., said there is work left for the U.S. courts. They could overturn the district judge and order Lynne Chafin to return with the child, he said. Or a subsequent decision could be influential on the Scottish courts. And there is still a live issue in the district court’s order that Jeffrey Chafin pay nearly $100,000 in lawyers’ fees and costs.

“There is a remedy that can be provided here,” Manely said. “It is not impossible.”

Several justices seemed to suggest that judges in such cases be more forthcoming with stays following their decisions, in order for the losing party to have time to appeal the decision before the child is removed to another country.

But that would be for the future and seems to have no effect on the present case, Chafin v. Chafin.