[Morthoron]

Rather than pull stray words out of a hat and put context where there is none, Tolkien the scholar would know the significance of Gawaine's green girdle is not its invincibility, but is rather symbolic of Gawaine's failure against the Green Knight.

Gawaine accepts the girdle from Lady Bertilak, and although he readily, almost fearfully, takes it, valuing survival over virtue (and surviving without honour is unchivalrous). Gawaine refers to the girdle as “falssyng" (which roughly equates to "treachery").

Thus, after the Green Knight forgives him for his treachery, Gawaine nobly wears the girdle ever after as the symbol of his loss of honour, evincing the quote "a man may hide his misdeed, but never erase it."

So for Tolkien to equate Bombadil's green girdle with Gawaine's green girdle is rather farcical, since neither match contextually except they are green and a girdle. Rather than pulling appalling parallels from one's appendages, take the line

"bright blue his jacket was and his boots were yellow, green were his girdle..."

as simply a metaphor for sky, grass and flowers.