I called them up to be sure that it was as simple as it seemed, but all I had to do was fill out
this form from the
support page, package it in with the headphones (headphones only, no 3.5mm adapter, case or anything) along with a print out of the amazon order invoice. That's it. No need to start up a repair process with them beforehand. They sent it back without saying a word to me a day after they received it and shipped it back under standard UPS shipping.
But they weren't actually new headphones. They just replaced the the earpads and the cable (which was the part that broke). What made me think it was a new pair is that it came back quite a bit looser fitting (not really loose, but it no longer clamps my ears as tight as it used to, which I like better).