Punctuating Quoted Questions in a Parenthetical Clause [duplicate]
Normally, no comma is needed and none allowed after a question mark (Think of a period in place of a Q. mark) - it will itself provide the punctuation expected of a comma.
In your case, the comma follows the closing quotes, and so is not in conflict with the "?". (As with the period here).
The only issue would be if your style guide insists the comma should be inside the pair of quotes. Then you'd have to drop the comma.