"Our" Kitty

So I think we've become foster owners for a sweet kitty. I call him Tuxedo. He's been showing up at our back door meowing and just sits there and watches us through the window. Graham wanted let him in (the poor kitty is just begging for attention) but I told him that was a bad idea and that he might truly become ours if he comes inside. Today we arrived home to find Tuxedo waiting at the front door. He let me pet him for awhile and then tried to dart into the house when I opened the door. After making it safely inside (without him), he just sat outside the door and meowed. He waited there for about 5 minutes before he gave up. Next thing I knew, I looked up to see that he'd migrated to the back door to see if his luck was any better from that side. Graham tried to feed him peanut butter--which I think is just wrong--but Tuxy wasn't interested (can cats have peanut butter?) I'm not quite sure what to do with him but he sure seems to be intrigued by us. Guess we have a peeping Tom Cat...