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The attempted seduction was not “an attempt to show flaw in Arthur's servant and the whole chivalric system”.
In no medieval romance does anyone ever declare that Arthur's chivalric system is perfect and that the knights who are part of this system are perfect. This is implied in the question, but is not true.
The attempted seduction was intended to tempt Gawain into falling beneath his own moral code and being less than perfectly courteous. The seduction itself rather failed, in that Bertilak’s wife only obtained a few kisses from Gawain, nothing more.
What succeeded was the giving of the green girdle to Gawain and Gawain then keeping it instead of turning it over to his host as part of his game. This giving of the green girdle was NOT part of the attempted seduction but another temptation entirely.