As Seen In: "New Amsterdam" (Season 1, Episode 4)
During her first appearance, Trudy functions more as a device that humanizes Pete—we see how his home life has shaped him into a petulant shit, and also see that he doesn't really know the woman he's recently married—and digs into Peggy.
When Peggy meets Trudy, it destroys the possibility of a future for her and Pete. Ultimately, this is a good thing, but in the moment it's hard to watch Peggy hurt. Trudy's unwavering poise is on display here, though.