Submit your member number and last name for 300 points. (HT: James R.)
Here’s an old submission page for 300 points whose fine print suggests it has expired.
I’ve never stayed at a La Quinta. From having read Lamar Muse’s excellent autobiography about his years as Southwest Airlines’ founding President, I recall the story of the La Quinta chain (its founder was a Southwest board member). Apparently the name derives from the founder’s search for the cheapest furnishings possible. They had a Southwestern motif, and so he chose a name to match.
Free points, of course, are free points. Even if the Urban Dictionary claims ‘La Quinta’ means “next to Denny’s.” Points convert to a variety of currencies although you need 6000 points to do so. You can also earn free points via their Facebook game.