after reading the note said the cat is doing this "delibratly" I immediately had visions of said cat performing a song and dance routine decked out with top hat, striped jacket and walking stick using the "spotlight" as a stage.
Get a mate to dress up as said cat. Both go round to neighbour and knock on the door. When they answer don't give them the opportunity to speak just start giving the 'cat' a bloody good bking, how inconiderate it is being etc etc then just leave.