ORIGINAL: GregH
Send him a letter and include a pic of you and your deer. Tell him how much you appreciate the opportunity to hunt his land and what it means to you. Then, to show your appreciation, tell him you'd be willing to clean up the property if he didn't mind.
I believe that this would show your appreciation better than a simple thank-you card because you took the time to compose the letter. It's more personal.
Greg hit it on the nuts! I would go this route if I was you.