They've handed out sealed envelopes randomly to Guests over the years. They're just a little bit of a "magical moment" for a few Guests a night. My friend got one in 2007 from the Maitre'd (whom I didn't see when I was there a few weeks ago. He's been at the AC for YEARS).
They're sealed envelopes with postage and addressed to the Club. Inside is a random letter from one club member to another. It appeared to be actually typed up on a manual typewriter and not printed out on a printer.
I saw four different letters (still sealed, I believe) being auctioned off on ebay last week.
Usually they'd only give a few out each night. My guess is that they had a ton left over, so they were handing them out freely on the last night.
-Rob