Supreme Court justices on Tuesday sounded skeptical that the government may force foreign affiliates of U.S.-based health organizations to adopt policies opposing prostitution if they wanted money to fight HIV/AIDS.

As the court held its second day of oral arguments via teleconference — again with minimal technological glitches and the formally reticent Justice Clarence Thomas joining in the questioning — justices returned to an issue it had partially addressed before.

In 2013, the court ruled that it violated the free speech rights of the health organizations to force them to “pledge allegiance” to the government’s point of view by having a policy “explicitly opposing prostitution and sex trafficking.”

In the view of the groups, that hindered their effectiveness, because combating HIV/AIDS meant engaging with sex workers.

But the new case involved the foreign affiliates of those U.S.-based organizations, and Justice Department lawyer Christopher G. Michel told the court that made a huge difference.

“Foreign entities lack constitutional rights, so they cannot bring an unconstitutional conditions claim,” Michel said. And the U.S.-based groups have nothing to complain about “thanks to their victory in this court.”

The groups “can choose to affiliate with foreign entities that must comply with the policy condition, but any effect on [the groups’] message is now a product of their own choice, not government compulsion.”

That question of whether the speech of the foreign entities could be attributed to the domestic organizations seemed key to the case.

Several justices who were in the majority in the 6 to 2 ruling in 2013 agreed the case raised new complications.

Chief Justice John G. Roberts Jr., who wrote the opinion in the 2013 case, did not sound as if he were among them.

“They have the same name, the same logo, the same brand,” Roberts told Michel. “And I wonder if it makes more sense to think of the foreign entity as simply another channel for the domestic entity’s speech.”

Justice Stephen G. Breyer told Michel that the court decided before it would undermine the integrity of the domestic organizations to force them to denounce prostitution while working with prostitutes.

“Since the foreign workers are identified by name, mission, logo, with the domestic workers, how does it interfere one whit less if we accept your argument?” Breyer asked. “They will be seen, domestic, as well as the foreign ones, as hypocrites or, worse, interfering with their mission. If we accepted that argument before, why don’t we accept it now?”

In response to a question from Justice Ruth Bader Ginsburg, Michel said the requirement did not affect how foreign organizations perform their jobs.

There is no requirement to “shout it from the mountaintops or get into anybody’s face about it,” he said. “They are completely free to, and encouraged to, work with prostitutes and victims of sex trafficking to prevent HIV/AIDS.”

He said the government has spent $80 billion on the effort, saving 17 million lives.

But David W. Bowker, representing the groups, said it is impossible to separate the message from the domestic organization from its foreign affiliate.

“When CARE in Kenya takes the pledge, its affirmation of belief is attributed to CARE in the United States, thus putting words in the mouth of the U.S. entity,” Bowker said.

Justice Neil M. Gorsuch questioned whether there was much evidence of that assertion.

Justice Samuel A. Alito Jr. noted that he voted with the majority in the last case but worried that doing so again would “force Congress either to withhold foreign aid entirely or to allow foreign aid to be used in ways that are contrary to the interests of the people of this country.”

Justice Brett M. Kavanaugh, who like Gorsuch was not on the court in 2013, said he worried about other implications. He wondered if agreeing with the groups would undermine the ban on campaign contributions from foreign interests, or whether the government could fund foreign organizations only if they agreed, for instance, to recognize the legitimacy of Israel.

Bowker said ruling for the groups in this case would not necessarily imply broader application.

“This particular requirement is unique,” the lawyer said. “There’s no other requirement like it in U.S. law. And I think a decision for [the groups] can be very narrow, turning on the facts of this case and the prior ruling of this court, which declared the policy requirement unconstitutional.”

As in the 2013 case, Justice Elena Kagan recused herself, likely because she worked on the issue while solicitor general in the Obama administration.

The case is U.S. Agency for International Development v. Alliance for Open Society International.