I have a little different policy.  Probably many different policies here.
Mine is, if it is wild and intruding on my property and doing damage and not protected by law, it is fair game.  It's going to get trapped and turned over to animal control, or disposed of.  
If it is domesticated, I think its not the animals fault and there is another way.
I would fence, electrify, charge the owners all costs plus a stupid tax, call the pound, call animal rescues to rehome the pet to more responsible owners (far far away), or rehome it myself to someone without chickens and with big strong fences.
As you can tell by my way too expensive, heavy-duty coop, I hope/pray to avoid these trials of conscience.