Whose cat is it? Just a neighbor's? When I lived in Boise, the guy who lived across the street from me had two outdoor cats, and they would do the same thing, lol. We didn't have a pet door, but those cats adored me, and they would constantly bring presents and leave them on our doorstep. And by 'presents' I mean 'dead things.' Which was sweet, in its own catty sort of way, but not terribly pleasant.

Maybe you could put a bowl of food for it outside? I guess, depending on whether it's hungry or just looking for attention. At which point you're screwed, because it probably isn't leaving.