weeeeeeeeeeeeeelllllll this is probably bollocks but someone once said they're bringing you live things in because they've twigged your hunting skills need some polishing and live things are what you need to practice on, what you need to do is pretend to catch it and eat it whilst surrepticiously surrepttisch slyly secreting it for later release and then the feline will think you've 'finally' learnt how to hunt and not bring anything more in.
However, with our hunter, I loudly told her to take it OUTSIDE AND PLAY WITH IT THERE and she's never brought anything else in again.