If it's not attacking your cat, who seems to regard it as good company, and it's not peeing in your house, then is it a problem? Would this uneaten food go stale and be thrown away if the dustbin cat didn't call, or is it eating the lot and leaving your cat hungry?
I had a female cat who used to sit and watch a male stray eat some of her food with the kind of loving satisfaction that looked like she had cooked it herself.
This cat may not be a true stray, and I'm sure you don't want to overencourage it if it belongs to someone else. If it only turns up at night that might be a nervous stray choosing the quietest time to raid your kitchen, or because it's living a truly nocturnal existence, or it may just be that some owners have put it out for the night and your house is on the nightly routine. A true stray, a hungry one, might be more likely to hang around during the day, near the food source, even if it won't dare enter your house then, so you would see it around a lot.
If you're sure it's a stray, in poor condition, rough coat, and it's always starving, then why not help. Put it this way, if your cat strayed, you would hope some other cat samaritan would do the same.
I have been feeding a 'stray' for years. There's never any leftovers to throw away with him around.