Sounds like "Black & White" is a cat, not a kitten, so the fact that it is comfortable coming in the house suggests it's a domesticated cat that no longer has a home. So it's not just about the food, it's about comfort and safety.

It could be lost so keep an eye our for "Have you seen" posters.

Despite the confrontation, it's possible that the cats aren't entirely unfriendly, otherwise B&W probably wouldn't have come in at all. Tess just doesn't want to give up her bed! If it is homeless and has decided you're the best option, don't expect it to give up too easily.