Congrats on your new loot.
I currently have a similar situation going on and so far have handled it differently than you, but if it goes on much longer I too may be having an early Christmas.
We have a nice sandbar where we've always been able to swim and fish. We've hosted hay rides and cooked hot dogs and smores on the sandbar and everyone loves it. (Of course the little kids HAVE to throw rocks it the creek.) The sandbar has changed for the worse due to road construction up the creek, but it"s still is a great place to enjoy the 4th of July and other days, when the mood hits. Across the creek is a bluff. On top of the bluff several homes have been built. I know that some of the neighbors or their kids have also been enjoying the sandbar (without permission).
Saturday, I decided to check on things at the sandbar. I found a tent set up with a couple of blankets inside, a couple of yard chairs, ashes from a fire, empty beer cans, a pair of wet blue jeans, some wet socks and two empty gas cans. I called and spoke with a couple of folks who have permission to be down there and it wasn't theirs.
I started to take the kids stuff (I think I know which kid it is and school is out this week) but decided to leave a note stressing that he needed to call me and take his trash home with him. (Under the theory that I can't be everywhere at all times, and I'd rather have an understanding with the guy than turn him into an enemy.)
Yesterday, the tent was still there. But he had kept the note. It was folded up and in the tent. (So at least he didn't burn it or throw it away, yet.) I unfolded the note and put it back in the handle of the gas can and put the can back inside the tent.)
I still haven't heard from him (SURPRISE, a 15 year old kid isn't all that responsible) so I'm currently debating with myself whether to take his stuff or to follow the 4 wheeler tracks back up the bluff to his house (with a few of his empty beer cans) and have a little face-to-face with him.
Personally, I'd rather he didn't drink down there, but if he takes his trash home then I won't know. I'd like for him to turn into one of those folks who are respectful of other folks property rather than one of those who thinks every open gate is an invitation to "come on in" and do whatever you feel like.
We'll soon see how this turns out.