Hmmm, interesting. I also love bg info and here are my thoughts:
1. Peyton worked in ME's office pre-911, so she might know Mac had a wife but at that time it was really more working relationship so she didn't necessarily know the detective's personal life in detail. Stella might knew Claire in person as she is Mac's working partner and friend. I even doubt whether Hawkes knew Claire in person. They might just only knew her name.
2. Peyton sort of leaving the Lab around 2001 to teach in Uni. She said in 307 that she spent 4 years with Hawkes in ME's office but the info from CBS said 2 years. Anyway I think when 911 happened she might have already left the ME's office. But she might heard about Mac's tragedy, from Hawkes maybe. She might even sent a card or whatever to express condolence as an old colleague or friend, but that was it.
3. At the end of season 1 Mac decided to move on, and later on, he and Peyton chance-encountered somewhere, maybe a conference. And that's how everything began. And then of course at some point I think Mac would talk about Claire with her.
I know I made lots of assumptions, so it's just a theory.