Tear Shed Down After or Before Closing?

Last time I had my home for sale, the agent leveraged repair items on me to lower my price. He figured I would lower it after repairs since he knew the buyer did not qualify for that amount but would not tell me that. So this time....this time, the new buyer wants me to tear down a shed which is Marginal in looks and use (it becomes a rental if I do not sale) ...It's under contract for me to tear it down (I agreed) My problem is: When do I tear it down? If I do now and the loan or sale falls through, then I'm looking like a fool with a torn down shed I could have used for the renters (if this falls through) The agents are making a big deal out of it...I don't trust agents/salesmen, Any ideas?