It was an obvious scam offering a bogus award (2 airline tickets), and I'm quite sure that if I called the phone number I would be asked for my credit card information.
A quick google search showed that I didn't even have to worry about scanning the letter so that you could see it. Here's one someone else got a few months back; the body of the letter is identical word-for-word except for the phone number.
The person who posted that image also made a detailed write-up on the scam.
What we have here is a scam that operates on two levels. The recipients of the letters are targeted of course. But so are the senders, probably in a work-from-home scam. The most flabbergasting thing about this scam is that the master scammers are actually convincing their agents to hand-address these letters and spend the money for first class postage.
I also found a youtube video about American Airways posted by, of all people, a man named William Cozantino (a big MLM promoter) who warns his viewers to steer clear. Ironically, in another video William bemoans the big bad gummint interfering with Zeek Rewards! His advice to Zeeksters: ride it out.
You know a scam is a scam when other scam artists raise the bullshit flag on it.