A contract with a minor cannot be enforced. Sgt Winslow should have told the buyer that information - thus no need for the long dialogue to get the quilt back.
Towards the end of the episode when Harriette is calling for Eddie and Judy to come downstairs after they got the quilt back you can see a shadow of camera equipment at the bottom left of the screen.
If Grandma Estelle had told Laura the history of the quilt she would have known why she couldn't sell it.