Bite a rat to death in front of the cat and consume it raw while maintaining unbroken eye contact.

... and after that Ozzy Osbourne's cats never brought him dead animals again. The end.

Interesting thought! You could take folks who regularly get dead animal presents and then have their cat witness them catch a rodent or bird, and see if the presents continue. I'd enjoy that read or youtube video, haha.

Leave an elk carcass on their pillow, that ought to shut them up.