This happened to me a few years ago on the Olmpic Peninsula. I had lost my anchor on some rocks in high water and finally giving up unsticking it I cut the rope quite long hoping to get it back during low water, but never did. Then many days later I spotted my anchor on the back of another boat. I asked if they found it up river and they agreed. I told them that it was mine and I would gladly give them the anchor I was now using and the one they had fit into the anchor cradle built into m drift boat. They agreed and the swap was made. I was happy to get it back and I guess they had no guilty feelings.
So I guess my answer to your question is "what do they have for a finders fee" or just give it back and be a good guy. I am sure I would give it back. fp2