I know. It's very sad for the little mice. Poor little Souls.
I am looking after someone's cat too, and she is a hunter. I am forever giving tiny mice decent burials and blessings for their journey into the afterlife.
My own feeling is, there is little you can do to control that except keep her constantly inside. And that is unfair to a cat who loves/needs to be outside. A cat has a wild streak and isn't actually meant to be kept bottled up in a living room for the rest of its life....well that's how I feel anyway. I am from UK where a totally "indoor cat" is almost unknown unless it is terminally ill.
I have seen the natural and happy life the cat I'm looking after has, and she craves being outside especially in decent weather. She has always lived like that. She would be extremely unhappy and neurotic locked up all day.
They are naturally hunters. That is their skill. We can't really project our values onto them.
The mice actually do have a chance. The ones that get killed haven't grasped their chance. I have heard mice noisily announcing their presence with squeaks.....
That is a dead giveaway.
Buzzards prey on them, as do Foxes and Sparrowhawks. It's not only cats.
But if she eats them, then do make sure she gets a multi-wormer as recommended. My dog used to get worms if she ate a mouse.