The title is from the musical 'Sweet Charity' by Cy Coleman, Dorothy Fields and Neil Simon. The original Broadway production of "Sweet Charity" opened at the Palace Theater on January 29, 1966, ran for 608 performances and was nominated for the 1966 Tony Award for the Best Musical. John McMartin reprises his role in the movie.
Mel mentions a new chick he met the night before at the Chez Chug a Lug named Marie, and brings her to the charity ball. In the previous episode "What are you Doing New Years Eve" Mel spends New Years with Marie and they are clearly together.