Just tell them that you need 20% down and only have enough money to cover this much.
I have no idea how the legality works when it comes to conditional offers. I had a realtor tell me that I should make a conditional offer on a house I didn't like to prove that I was serious. She said not to worry about the offer because you can just say financing fell through and back away. (I fired her a few minutes later though so I don't have any faith in her advice.)
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