According to the Arthurian legends, Gawain is Arthur’s nephew by his half-sister, Morgause, and King Lot of Orkney (source).
The deer-butchering scene in the poem describes how the butcher "rapidly separate the sides from the chine" (1353). What is the chine? According to yourdictionary.com, it’s "a cut of meat containing part of the backbone" (source).
We were wondering if the Jolly Green Giant, the mascot of the Green Giant canned and frozen produce company, was inspired by the Green Knight. Their website says he's "inspired by folklore and fairy tales" (source). So, we're not exactly sure, but we kind of think our hunch is right.