Reilly's girlfriend is a woman who is subject of various conversations regarding her name, notably after Reilly is killed by Scar.
After Reilly's death, Louanne Katraine takes it upon herself to find out this woman's name believing it important for sentimental reasons, but ultimately fails to do so.
During conversations in the pilot's duty locker, Tucker Clellan offers his belief that she died on Picon and that her name may have been Karen. Brendan Costanza believes her name is Kathy, while later, prior to destroying Scar herself, Katraine believes that the girlfriend may have been named Kassie. During the various instances that Kara Thrace hears Katraine broaching the subject, Thrace strongly rebukes her efforts, claiming it of no importance (TRS: "Scar").
The picture that Katraine retrieves from Reilly's bunk is later added to the memorial hallway, and later accompanies both Katraine's and Thrace's pictures (TRS: "Scar," "The Passage," "The Son Also Rises," "He That Believeth in Me").