It is illegal to own an american aligator in the state of texas, my grandfathers ranch has one on it...?

Your grandfather should definitely have a talk with them. That is ridiculous that he would get fined at all because there is an alligator in his pond. I would be very upset if I were him, under what idea do they think its his? Just because its his pond means nothing. Make sure you do NOT feed it, to be honest, I would recommend you shoot it if possible.