In the episode Billboard, Hal was being interviewed on the news and talked about his mother. He explained how she was very smart and also extremely hard-working and she always worked in the kitchen. It is unknown if this was true, or he only said this for the cameras.
In the episode Living Will, Claire was briefly seen from behind in a flashback, of Hal's childhood. She told Hal that for his birthday, he had to make a decision between a clown and a petting zoo. She had blonde hair, worn in a bun, and a white dress.