I believe there IS a pet door that is operated remotely by a signal on the cat's collar, letting only your cat in, but I bet it is very expensive!

My three cats are inside/outide also, but I leave the garage door up a few inches for them to come and go. Last night i heard the most chilling howls coming from my garage...Another cat had ventured in and my cats were "asserting" themselves. This rarely happens because they do seem to guard their territory.

This cat that is coming in thru the pet door...Do you think he is an un-neutered male? Marking his territory sounds like it.

I wouldn't know what to do in this situation.
Patty