Yeah, isn’t it funny how people want to tell you what you’re allowed to do on your own property?
If my dogs got loose and we’re on your property, I would hope that you’d try to contact me via the phone numbers on their collars. But, if for whatever reason you needed to shoot them I would be very upset. I have invested a lot of time and money training my dogs and I love them, but I am reasonable enough to know that they were on YOUR property and you have a right to do with your property as you see fit.
if it is an ongoing thing i might be inclined to call animal control or catch it and give it to somebody on a farm that might appreciate it
if it takes an aggressive posture, well, all bets are off...