@sirwolfeye Pretty sure there isn't a joke at all, it's just vaguely poignant because she is helping them get together even though it means her own christmas eve ends up lonely.
She claims to already have plans with her family so they should spend the day with just the two of them, but when she calls her mom it reveals she was lying and will actually just be her and her brother waiting for their mom to get back from work.
The title "気を遣おう!" usually means "Be Careful!" but in this context it means "Be Considerate!"(don't be a third wheel to the couple).