No - "overdue" is enough, and "past" would be wrong here. You could also say "which is": "Please let us have your check for the $60 which is now overdue."

Possible sentences: 1) "Please let us have your check for the $60, now overdue." 2) "Please let us have your check for the $60, now past due." These 2 both suggest that the check was not given by the due date. "Overdue" and "past due" are usually interchangeable. However, people typically prefer one over the other for different things. For example, it sounds more natural to say "an overdue library book" and "the rent is past due". 3) "Please let us have your check for the $60, now long overdue." "Long overdue" emphasizes that the check was not given by the due date AND that a long time has already passed since the due date.