He showed them the wound in the neck which he won for his disloyalty at the hand of the knight, the blood flew to his face for shame as he told the tale.
Gawain has gone through with his quest despite the guide offering to not say anything if he didn't. Gawain has proven his chivalry, honor, and honesty as a Knight and person when he honestly relays his travels while wearing genuine shame on his face. "Arthur, Guenevere and the others gaily laugh at him, seeking to diminish his shame and wanting to integrate him back into Camelot".(Trigg) By honoring his role as a Knight despite carrying shame about his actions, Gawain has learned and therefore is rewarded with unquestioning acceptance back to the roundtable.
Professor Stephanie Trigg, University of Melbourne. “The Poem behind the Green Knight.” Pursuit, The University of Melbourne, 4 Mar. 2024, pursuit.unimelb.edu.au/articles/the-poem-behind-the-green-knight.