Quote 1
"So good a knight as Gawain as rightly reputed,
In whom courtesy is so completely embodied,
Could not easily have spent so much time with a lady
Without begging a kiss, to comply with politeness,
By some hint or suggestion at the end of a remark."
(1296 - 1301)
The lady’s implication here is that Gawain would be breaking the rules of courtesy not to seek a kiss from a lady who has asked for it with her flirtatious manner. Gawain is really in a bind now, because to reject the lady’s advance so overtly would certainly break the rules of courtesy, while to become romantically involved with her would be to betray Lord Bertilak and break the code of knightly conduct.
Quote 2
"Sir, if you are Gawain, it astonishes me
That a man always so inclined to good,
Cannot grasp the rules of polite behaviour,
And if someone instructs him, lets them drop out of mind.
You have quickly forgotten what I taught you yesterday
[. . .] about kissing," the fair lady replied,
"To act quickly wherever a glance of favour is seen;
That befits every knight who practises courtesy."
(1481 - 1485, 1489 - 1491)
The lady of the castle uses the "rules of polite behavior" to trap Gawain into kissing her. According to her, these rules dictate that a knight must always be quick to kiss a lady when her flirtatious behavior indicates she wants him to. Gawain has even less wiggle-room once the lady has stated this bluntly, however; were he to say no at this point he would really be rejecting her.
Quote 3
"So good a knight as Gawain is rightly reputed
In whom courtesy is so completely embodied,
Could not easily have spent so much time with a lady
Without begging a kiss, to comply with politeness,
By some hint or suggestion at the end of a remark."
(1297 - 1301)
As the Green Knight did before Arthur’s court, Lady Bertilak uses a particular reputation - here, one for courtesy - to force a desired behavior from her prey. Like Arthur’s court, who risked besmirching their reputation for bravery if they failed to comply with the Green Knight’s game, Gawain must comply with the lady’s wishes or risk damaging his reputation for courtesy. Yet Lady Bertilak takes it one step further by implying that Gawain is not Gawain if he fails to comply.