As Harvard prepares to defend its race-conscious admissions program at the Supreme Court this month, a federal judge in Boston is considering a related dispute arising from a fumbled insurance filing, one that could cost the university $15 million.

Harvard failed to file a timely formal claim with one of its insurance companies for its expenses in defending the lawsuit challenging its admissions policies. That company, Zurich American Insurance, refused to pay, and Harvard sued. In the process, the university disclosed that its legal fees and expenses in the admissions lawsuit and a related Justice Department investigation had topped $27 million.

“One of the nation’s top universities is apparently not great about doing its homework,” said David Lat, a legal commentator.