Yes, the university you attended may condition issuance of a diploma on you first fulfilling your obligations, even an obligation to a sister university made through the one you attended.
As a simple matter of right and wrong, though, when you borrowed the books through your university, you implicitly agreed to return them timely or pay late charges. Seems to me you should do the right thing: pay the late fees and move on.
Congratulations on completing your course requirements, and best wishes,
Scott J. Summer, Staff General Counsel
