Apparently, Rose Carson was a real dish when she was younger, kind of like that lady from Titanic. We know this because Tom Browning seems to still have a serious thing for her. They have a major history: "They'd talk about a time when some guy and girl got caught making out on the hayride, and then suddenly they'd be talking about how nice his funeral was" (10.56), Karl says. Yeah, these two go way back.
Maybe she's not a major character in the book, but the relationship between Rose and Mr. Browning definitely gets Karl thinking about the importance of friendship. What interests him about their friendship is that even though it's been a long time since they last met up, it's like they've picked up right where they left off. "They hadn't seen each other in more than a year," Karl observes. "I mean, how can you let a friend go for that long, especially when you only live like twenty minutes apart?" (10.63). Perhaps his encounter with Browning and Rose is the beginning of Karl's reconsideration of his decision to ditch the Madmen.