In fact, it was the working title of a song Paul Simon was then writing. But the “Mrs. Robinson” in that song wasn’t a fictional movie character. Who was Simon singing about?
Well, at least initially, Eleanor Roosevelt (but no, not in that way).
According to a Variety article by Peter Bart in the May 15, 2005 issue, director Mike Nichols had become obsessed with Simon & Garfunkel’s music while shooting the film. Larry Turman, his producer, made a deal for Simon to write three new songs for the movie. By the time they were nearly finished editing the film, Simon had only written one new song. Nichols begged him for more but Simon, who was touring constantly, told him he didn’t have the time. He did play him a few notes of a new song he had been working on; “It’s not for the movie… it’s a song about times past — about Mrs. Roosevelt and Joe DiMaggio and stuff.” Nichols advised Simon, “It’s now about Mrs. Robinson, not Mrs. Roosevelt.”
Note that the song as it appears in the film is different from the hit single version, as only the chorus of the song appears multiple times throughout the second half of the film. It was only later on that Paul Simon and Art Garfunkel re-recorded the song, expanding it with additional lyrics to form the hit single. – – – source Wikipedia