I'm very sorry to hear about your loss.
It breaks my heart when I lost a kitty, they are so much my babies.
Last time I lost a pet to someone's dog, I marched up with my dead animal to their front door, banged on the door with tears rolling down my face and explained to them how my pet died. They thought I was nuts until someone went looking for the dog that "never goes outside unless we're with him" and they couldn't find him. When said dog was finally found, he still had blood on his muzzle.
Again, I'm sorry. You might let the owners of the greyhound know what happened to your cat. Try to take it easy, I know that's not much help, but try.