If me, I would go over with a box of donuts, tell the guy I'm sorry for the mess (even if I don't really mean it) tell him it's a peace offering and let him know I intend to make sure my landscaper won't leave a mess on his yard again. You may or may not gain some respect from him for trying to be a good neighbor, but at least he won't see you as a total **** and make your life a living hell. Making enemy with your cop neighbor isn't a smart move IMO.
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