Schelling on dealing with threats:

“[I]f the person to be threatened is already committed, the one who would threaten cannot deter with his threat, he can only make certain the mutually disastrous consequences that he threatens.”

With “person” equal to professor and “the one” equal to student, Schelling adds:

“At Yale the faculty is protected by a rule that denies instructors the power to change a course grade once it has been recorded.”

Does Yale still have this rule?  The threatener can apply a threat at a higher university level and not directly at the professor.  Ideally, the threatener’s parents – the ones who sign the checks –  can apply the threat.  Then the rule will be changed and you can turn your attention back to the professor.