Red velvet drapes hang at the back of the courtroom at the U.S. Supreme Court building in Washington, D.C. (Jonathan Ernst/Reuters)

With a conservative majority back in place, the Supreme Court on Thursday announced that it will once again hear a challenge to the required payment of fees to ­public-employee unions, an important but controversial tool for the American labor movement.

Some public employees say their free-speech rights are violated by the requirement, and conservative legal activists have at least twice asked the Supreme Court to overturn a decades-old precedent that allows “agency fees.” Approximately 20 states allow them.

It appeared the challenge would be successful the last time the issue was before the court, in January 2016. But Justice Antonin Scalia died a month later, and the court announced that it had split 4 to 4 on the issue.

Now Justice Neil M. Gorsuch has taken Scalia’s place, and the groups advocating for the change are hopeful he will provide the fifth vote.

“We are now one step closer to freeing over 5 million public sector teachers, police officers, firefighters, and other employees from the injustice of being forced to subsidize a union as a condition of working for their own government,” Mark Mix, president of the National Right to Work Legal Defense Foundation, said in a statement.

The lead plaintiff in the case the court accepted is Mark Janus, a child-support specialist at the Illinois Department of Healthcare and Family Services.

Union leaders responded to the court’s decision to take the case by saying the real players behind the effort are those who want to blunt the effect of public-employee unions, the most muscular part of today’s labor movement.

“The Janus case is a blatantly political and well-funded plot to use the highest court in the land to further rig the economic rules against everyday working people,” said Lee Saunders, president of the American Federation of State, County and Municipal Employees.

“The billionaire CEOs and corporate interests behind this case, and the politicians who do their bidding, have teamed up to deliver yet another attack on working people by striking at the freedom to come together in strong unions,” he said.

The case involves only ­public-employee unions — not private workers — but those unions are the strongest segment of an organized labor movement that is increasingly tied to the Demo­cratic Party. At the same time, Republican governors across the nation have become embroiled in high-profile battles with the ­public-employee unions in their states.

Challengers are directly asking the court to overturn a 1977 decision, Abood v. Detroit Board of Education, that favored the unions. That ruling said states could allow public-employee unions to collect fees from nonmembers to cover the costs of workplace negotiations but not the union’s political activities.

The unions say losing those fees would be a heavy blow because there is no incentive for workers to pay for collective-bargaining representation they could receive free. About 20 states, including California, allow what the unions like to call “fair-share” fees.

But conservative justices have sharply questioned whether it is possible to separate public- employee negotiations from the kind of public-policy questions — teacher salaries and classroom sizes, for instance, and the tax dollars needed to pay for them — that are raised.

The case is Janus v. AFSCME Council 31.