First of all, Cappy, I dunno what TX laws are in regards to reptiles, but I know that in some places it is not legal to kill turtles, and in other places it's frowned upon. This may be regardless of whether it's your own private property or not. Chances are killing 'em won't be caught by the AHJ (authority having jurisdiction), but if it is, it could result in some ugly fines.
In regards to you or gramma catching them, you're bolder than me. I have some wierd hangups about handling certain animals. I have no problem handling a gar or pickerel, but am terrified of catfish. I'll handle toads, but not frogs. In much the same vein, I have little fear of snakes (even the "bad" kind), but am pretty petrified of turtles.
