I suppose the non-toxic restriction eliminates most .22 ammo. That would disqualify the most likely gun to be around the house.
And if they're an invasive species and unprotected, why bother with that kind of nonsense? It's not like they're shooting in a regular hunting area which would have decades of lead shot lying around, and I'm fairly sure there'd be no danger to Condors in Texas. And if they're unprotected, why can't folks eat them?
After all, if they're an invasive species, they can't be owned by the people of the State, like regular wildlife, so why can't one sell or eat them?