The ZFT has gone after tribute bands for years - calling clubs where they were performing and claiming that the bands/clubs weren't covered by their usual licensing agreements to play Frank's music. Dweezil was the public face of that stance. Since Gail's death, I've come to mostly think that he was spouting the company line - I didn't realize she was charging him a nominal fee to use the name Zappa Plays Zappa, or that she was taking 50% of merchandising (while not paying DZ his share).
Reading about some of the stuff Gail did to Dweezil and Moon makes me shake my head. And for Ahmet and Diva to continue that...