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By secretly accepting the girdle and refusing to give it away, Gawain violates the agreement he had with his lord thereby violating the chivalric code of honor that binds such contracts. It is not nearly as great a violation as adultery would have been, but it nevertheless shatters the code of chivalry which Gawain lives by. Thus, where the lady failed to seduce Gawain by appealing to his desire for sex, she succeeds by appealing to his desire to live. Both are basic animal instincts, and while Gawain can smother the one through his strong moral sense, he cannot ultimately ignore the other: the fear of death hangs too much on him. In this way, the idealistic Gawain finally allows himself to be guided by his own nature, and not by his sense of societal duty.
No he shouldn't've take it . . . that was wrong.