Put it to your insurance company with a full statement that the child opened the door. They are probably claiming for damage to the door rather than injury. Don't forget that the first line for any claim is that it was the other person's fault, but it's up to them to prove that you are liable, not for you to prove your note. Don't respond other than to say you've forwarded it to your insurance company - this is what you pay your premium for, let them fight it for you.