The Mona Lisa was stolen from the Louvre on August 21, 1911 while Eliot was still in Europe following his year at the Sorbonne. The theft and its hullabaloo may have made a big impression on him. It turns out that the painting was stolen on Monday morning by just being removed from the wall. It was not discovered to be missing until Tuesday afternoon!
There is a PBS half-hour documentary covering the theft of the Mona Lisa. The documentary is part of a series entitled "Treasures of the World". Perhaps your PBS station may be having a rebroadcast soon. (PBS is America's Public Broadcasting System.)
There is a theory that the Mona Lisa is a fantasy self-portrait of Da Vinci (and thus the mischievous smile.)
A researcher found that if she scaled down a drawing taken to be Leonardo's self-portrait and then flipped the image left-to-right the face matched that of Mona Lisa's. The juxtaposition was discovered by Lillian F. Schwartz. The combination of the portraits can be found at two web pages listed below. (Leonardo kept the painting of Mona Lisa until he died.)
See Smithsonian Magazine, May 1999, p. 54, "Seeking Mona Lisa" for more on the painting, it's theft and a little on Schwartz.