Entirely personal preference. I would not relocate it and run the risk of it returning or having a go at me while I tried to move it. Same goes for stray dogs. I have a lot of money invested in my livestock and I won't tolerate anything taking an easy meal.
I detest killing things, but Im squeemish as hell about germs. Imagine the shennanigans involved getting that Hav-a-heart into the car!