The financial letter is irrelevant here

Whatever it states of your purchasing power is irrelevant, unless you guys incorporated into your purchase contract. Now the only thing you need to read is the escape clause in the purchase contract, specifically the mortgage contingency clause. I believe most of such contract will allow the buyer to walk away unscratched if he/she cannot obtain mortgage on a specific amount with a reasonable interest rate within the given timeframe. Yes, the interest rate they quoted you may be high. But as long as it is reasonable within this market, you have no case. Anything below 8% would almost certainly to be considered reasonable in the court.

The other you may want to try is to argue that you rely on his representation that you could obtain 4.35% from the local bank. But I don't think you guys have anything in writing to prove that.

Just pay the money and move on.