I would imagine it is straight forward. Owls are similar to snakes and frogs in that prey is alive. You can with time train snakes to eat dead mice. It can take a long while. You can't with frogs. I'd imagine owls are similar; they can be trained but it goes against their instincts. You're then faced with letting perhaps already injured or sick birds die because of a moral dilemma. The ethical dilemma makes it clear though; a few mice out of billions to perhaps allow the gene pool of the owl to remain viable. And since in the field I see birds of prey catching creatures not keen on dying every day, I don't see it as an issue. More so having shared house with rats and mice.. I don't hate them and not do I wish them to suffer. But ecosystems exist because there is brutality in nature. There are none that work with only vegetarians. Along side that, there's no clear evidence that plants feel nothing from being consumed either. It is merely life.