Think about that for a sec - we're talking about taking away a beloved pet because it is inconvenient, and the owner seems difficult to deal with. I dunno about you, but I've had pets stolen before, and it isnt' fun. Think about that as you consider your course of action. What woudl happen if someone made sure your dog or cat went away and never returned.
No, we're talking about taking away an animal from an owner who is not respectful of her responsibility to the community.
The cat is:
1) on someone else's property.
2) leaving behind rotting corpses that the property owner must clean up. In addition, killing the birds makes the cat a disease vector for anything the dead birds were carrying - ticks, fleas, viruses, parasites, etc., as well as attracting flies, rats, and other carrion eaters.
3) leaving behind fecal matter that the property owner must clean up- another disease vector and a smelly mess besides.
4) if the cat hasn't been "fixed" it can potentially add to the stray/feral cat problem. If you don't know, ask your local animal shelter about how bad it is and what happens to cats without owners.
Don't get me wrong- I'm constantly rescuing other people's pets where I live. I see a stray and I'll catch it and do my best to return it to the owner.
HOWEVER- this owner is irresponsible. She doesn't deserve the pet.