The National Labor Relations Board should scrap the contentious Obama-era test for determining joint employer liability despite a federal appeals court ruling that largely upheld that standard, the agency’s lawyers said.

NLRB General Counsel Peter Robb “strongly believes” that the U.S. Court of Appeals for the District of Columbia Circuit may have exceeded its authority when it appeared to direct the board to set a joint employer standard consistent with the court’s reading of common law, according to a brief...