The Neighborhood kitties might be ferals and thats what they do to protect their territory.
Keep the kitty inside.
I feed a few feral cats, even have 2 houses for them with heated beds, but I never let my cats outside because of the ferals out there.
Feeding the ferals and doing the trap, spay/neuter/release has helped to keep less feral cats in the area, because they will always protect their territory and stop other cats from being there.