Not quite. The Green Knight was sneaky, so he came up with some tests that Gawain had to pass before they met again a year later. He passes most of them, but he keeps a sash he got from a lady even though he was supposed to give everythin' he received to her lord husband in exchange for all the game the lord hunted during the day. After that, he keeps the sash to remind himself that he didn't keep his promise, and all the knights of the Round Table start wearin' green sashes to remind themselves to always be honest.