I haven't seen it posted there yet but you can check back on the newsgroup alt.fans.letterman
From the FAQ on the CBS website:
I missed an episode of the LATE SHOW. Can I order a copy from the show?
Sorry, but we are unable to provide any videotape copies of previous episodes of the LATE SHOW. However, we suggest you visit the "alt.fan.letterman" Internet newsgroup and post a request for the specific show you need there. Chances are good that someone will see your message and be willing to provide you with a copy of their own tape.
So I don't think it's illegal if they are suggesting it.