The Supreme Court’s 5-4 ruling in the Alien Enemies Act case raises open questions about how it will affect the Trump administration’s deportation efforts and the ability of targets of those efforts to fight back in court. But another question is what (if anything) it means for the technically separate litigation over whether officials violated U.S. District Judge James Boasberg’s orders in this case.

In a court filing to Boasberg after Monday night’s Supreme Court ruling, Justice Department lawyers told him that they think the ruling “eliminates the basis for this Court’s order to show cause,” referring to Boasberg’s order for the government to explain why it hadn’t violated his temporary restraining orders. At a hearing last week, DOJ lawyer Drew Ensign had a hard time giving the chief federal judge in Washington, D.C., satisfactory answers about the government’s conduct in failing to return alleged Venezuelan gang members to the U.S. from flights to El Salvador last month. The judge said he would issue a ruling on the compliance matter and possible contempt proceedings; that ruling could still come anytime, because it is a separate issue from what the Supreme Court just ruled on.

The high court majority vacated Boasberg’s restraining orders and said that D.C. is the wrong court venue (because the detainees aren’t confined there) and that the plaintiffs’ claims must be brought through a different (more legally restrictive) mechanism called habeas corpus.

But as a general matter, the fact that a court order is later overturned doesn’t mean that a party to the litigation was allowed to violate the order.

Boasberg previously pointed this out when he rejected the government’s argument that he should pause his orders because the DOJ was appealing them. He said he was seeking information “to determine whether the Government complied” with his orders and noted that whether the orders are “legally defective or legally sound does not govern the compliance inquiry.” Boasberg cited Supreme Court precedent that he said makes it “crystal clear” that “the proper recourse for a party subject to an injunction it believes is legally flawed — and is indeed later shown to be so flawed — is appellate review, not disobedience.”

We’ve now had (emergency) appellate review, but the obedience question is unresolved. Will it vanish along with Boasberg’s orders themselves? The Supreme Court could wind up addressing that question, too, but whether it proceeds on that course will depend on what Boasberg does next.

Subscribe to the Deadline: Legal Newsletter for expert analysis on the top legal stories of the week, including updates from the Supreme Court and developments in the Trump administration’s legal cases.