“they don’t kill them, just capture and relocate”
You might want to do a little more research...
Under Florida law, it’s a third-degree felony to kill or injure an alligator, so don’t try to poison or harm one to get rid of it.
In Georgia, Alabama, Arkansas, Mississippi, Louisiana, South Carolina, and Texas, you are required to obtain a license or permit to kill wild alligators.
In Florida, however, alligators can only be killed if deemed a nuisance by the Florida Fish and Wildlife Conservation Commission.
If the gator can be safely captured and relocated, then that is what they do...................