If you've executed an AAR Residential Purchase Contract, look at Section 3F which is the escrow company's instructions in the event of a dispute over the earnest deposit. Talk to the escrow company's branch manager, who is authorized in their sole discretion to make the call when earnest money is disputed. Find out their opinion on the situation. Then you'll have a better idea how to proceed--and if you need a RE attorney.
You could also notify the seller that you choose not to continue with the purchase because you cannot obtain financing without conditions, the conditions being the tree damage. At this point they may decide to grant you the extension until the tree damage has been corrected plus a few days for the lender/ appraiser to confirm this. Once the damage has been repaired and the lending condition resolved, you will be able to proceed with the closing.
I hope the title company is one that you chose to use, because in the event of an earnest money dispute, they are the ones that decide who receives it.
You may want to have your agent talk with the seller's agent and/ or their broker to attempt to resolve this matter before it goes too far.
Please seek the advice of a real estate attorney before proceeding. Best of luck!
Nobody here knows the terms/conditions you agreed to, and as such, nobody here can advise you what to do other than to have this discussion with your Buyer's Agent that you hired to help you with that purchase or consult a real estate attorney to review your P & S agreement.
PAUL WELDEN PLLC
Exclusive Buyer's Agent