Chris Parker is a Time Lady who used the Chameleon Arch on herself, and ended up on 1980s Earth. She wears the scarf because it makes her feel comfortable (a buried memory of either Romana or the Doctor), although the use of a huge fur coat as a disguise weighs the evidence closer to the Doctor. Brenda's reaction to the people in the subway station hints at an incident on Gallifrey that may have led to the Arch's use — especially the crazy young man, who looks enough like the Master of lore that Brenda is afraid the Time Lords have found her and Chris.