The moment
At a quiet moment, ask what first brought her to the game. The answer may be a neighbor, a grandmother, a new city, or simply a good invitation.
A useful detail
Listen for the ordinary detail. It is often more charming than a grand origin story and tells you what the table means to her.
Keep it human
Share your own answer if she asks. A group becomes warmer when people know a little of why they chose this room.
Let the person be the point.
A gift is optional; a sales link never replaces a useful gesture.