Greene and Letterman seemed to have a nice banter for probably 7-8 minutes. Letterman asked about topics that one would reasonably associate with physics (e.g., Einstein, what science has to say about the origin of the universe). I think it was when Greene was talking about string theory -- about how, at a level smaller than atoms and quarks, things might be comprised of strings -- Letterman asked him, in that mischievous way, "How is my life the better for knowing that?" (paraphrased).
Greene has a good sense of wit and timing, so he rolled with it pretty well.