If the high court sides with Starbucks, it could make it tougher for the agency to step in when it alleges corporate interference in unionization efforts.
The issue has vexed the court for months, with media stories focused Justice Clarence Thomas and his failure to disclose travel and other financial ties.
The case was the latest embarrassment for the CIA, which has seen a reckoning over its often secretive and antiquated handling of sexual misconduct claims.