I throw them away if the fur starts coming off - Hanna's ususally get wet though, she likes putting them in water. I have started to take the tails off right away too, because they are disappearing, and I suspect Hanna is eating the tails - I found one in a pile of puke. Other missing tails I haven't found. They come off easily, and she still likes the tailless mice.

I did buy her a larger fur toy (the weezil) and the fur came off - I did glue that back on.