The Trump Taj Mahal filed for bankruptcy in 2014 and was eventually taken over by billionaire Carl Icahn.
The Trump organization sought and won an order from a bankruptcy judge that ended the health insurance plan that had been negotiated with the casino workers' union.
Lawyers for the union challenged the order on the grounds that it violated federal labor laws. They won support from the National Labor Relations Board, but a federal appeals court in Philadelphia upheld the bankruptcy order and said it was needed to keep the casino in operation.
The union, Unite Here Local 54, asked the high court to review that decision, but the justices said in a brief order they would not hear the case of Unite Here vs. Trump Entertainment Resorts.