Remember the last gift that the Lady gives Gawain is the scarf, which she says will protect him. He is supposed to give every gift she gives him directly toward Lord (ugh, forgot his name--the one who is also secretly the Green Knight!)
The only reason he doesn't give the scarf to Lord What's-his-name is that he knows the Green Knight is going to chop his head off, so he needs the protection. So Lord/Green Knight was just testing him, and his victory in the bargain/bet is enough--he knows that Gawain is brave and honorable, and now that Lord/Green Knight has had some fun with him, he lets him off the hook.
Matt in NY