Markham Reynolds returns Juliet's letter and thanks her for catching the delivery boy; this means he doesn't have to try to arrange some way to meet Juliet a party. He explains that the Izzy Bickerstaff columns were the only things written by women that made him laugh during the war, and he wants to meet Juliet. He invites her to have dinner next week.
Notice that Mark seems to believe that he couldn't just have written Juliet; he needs to devise a plan to meet her "by chance." This allows him to feel more powerful and sneaky. His interest in Juliet because of the Izzy columns also suggests that he's interested in a fictional version of Juliet, not the real Juliet.