The passage that shows Sir Gawain's honesty and modesty is
The excerpt shows that Sir Gawain acted very incorrectly and brought about bad results, which Sir Gawain acknowledges were his fault.
Recognizing this, Sir Gawain shows himself to be an honest man who does not try to run from his mistakes. He also shows modesty, as he shows that he is willing to reward those who have been harmed by his actions.
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