Can you sue or file auto insu claim in FL after it was settled outside insurance and police weren't informed?

My wife hit a car that was in her blind spot. It was a minor accident with couple of scratchs and no bodily injury.So the other driver offered to settle outside insurance and police werent informed. My wife paid $250 in check and no other information has been exchanged. Can they comeback and ask for more money or can they file a claim??