Sorry to hear about your cat DC. Is there any news from the vet yet?
We know a bit about this, our Saluki Lurcher killed a cat while we were out walking. The dog was on a lead, the cat ran out under him and he just grabbed it and shook it. It took us a moment or two to get him to let go. He's an ex working Lurcher from Ireland and we all know how they are trained!
The cat people came out and yelled a lot at us. I said that I would give them a call to see how they got on at the vet. They seemed a bit confused by this as they didn't appear to actually have a vet and asked which vet they should ring. I told them they should call their own vet. The number they gave me was non existent and just went beeeeeeep when I rang it a couple of hours later.
They went to the papers and all sorts and then came round our house and threw bricks etc, yelling and screaming. They took us to court where we were told to pay about £50 of their costs. We were scandalised by their behaviour. They had kept that cat alive for over 48 hours at the emergency vets despite a catalogue of injuries. The court saw the vet report stating that the vet advised euthanasia but the owners insisted that the cat was 'fixed'.
For coridal neighbourly relations, if the cat in question is insured, asking for the vet bill nicely could be the way to go, after all they had 'got out' of their home and were not under control. Even if they just agree to pay the insurance excess. Most Greyhound owners I know are very responsible as their owners know of their high prey drive. 4000 years of breeding makes them a little interesting around small furries.