I must admit. That I have stolen a stand... It was a climber that was sitting at the base of a tree on the land I hunt on (my in-laws private land). I asked everyone who hunted there (family only), wasn't anyone's. So I went back and took it and gave it to my wife's cousin. I wish I could have seen the dudes face when he came back for his morning hunt.
I feel your pain. Had a visit from the cleaners myself. Just one time I would like to catch someone but it is probably better if I don't.
Removing a trespassers stand from private property is a little different. I have taken down a climber from someone that I know was trespassing and took it apart in pieces. Then I left a note for the person saying next time his stand would be removed. I found the stand 200 yards away on the private land, which wasn't mine, so I did the same thing. Never seen it again after that. If it was MY land, I would've removed it the very first time.
Better than a piece of paper stuck in the tube would be one of the Bluetooth stick on tracking devices, like stick n find or similar. They are small and can be easily hidden. Then you are not only relying on a positive id from a game camera. You can provide local law enforcement with a physical location of the stolen stand when tracked using a smartphone.
I actually had a conversation with a close friend. He thought it was perfectly acceptable to take a stand left in the woods. He was an otherwise ethical, thoughtful and great guy. Try as I may, he just refused to equate taking someone else's' stand with theft. Of course we weren't talking about private property in his case but that does seem to be the mentality of many stand thieves. In their mind they tend to rationalize: "Someone didn't care about their property or they wouldn't have left it... finders keepers... losers weepers!" I hope you catch and prosecute him... good luck.
I know you wouldn't... when I see one... I try to respect that person's trail. But there are some... many... who will take them.