Cats may be natural predators and prowlers, but mine only likes to go outside to roll in the sun and eat grass. She doesn't know how to "use the restroom" out of doors, and if she's accidentally gotten out for a few hours, she runs to the litterbox first thing upon entering the house.

Shouting when she starts to claw something of value works quite nicely, and we all get our exercise chasing her away from my LPS. (Which the dog really seems to enjoy.)

I'd much rather folks let their cats roam than their dogs, although we have a fair share in our neighborhood who do both.

Weepiper, I do think you should go to the authorities with this, simply because it's trespassing, if nothing else. Hope you find the "perps."