Might Want To Avoid "May" In The Past ;)

"Had he treated her with respect and dignity, she may not have cut him off."  "May" is incorrect here.  Notice that the cutting off lies in the definite past, as does his not having treated her right.  So, the correct verb is "might."

Here are examples where "may" is correct:

If he treats her with respect and dignity, she may put up with some of his quirks.

If they built that nuclear power station near the military facility, in the event of war, it may easily become the target of an attack.

Contrast that 2nd example with this:  If they had built that nuclear power station near the military facility, in the event of war, it might have easily become the target of an attack.