Final answer:
Sir Gawain keeps the green sash as a secret weapon, believing it will protect him when he confronts the Green Knight, which reflects his internal struggle and contributes to the moral lessons of the poem.
Step-by-step explanation:
The reason Sir Gawain keeps the green sash the lady gives him is as a secret weapon against the Green Knight. The lady convinces Gawain that the sash has magical powers that will protect him from harm.
Despite being a symbol of his failure to be completely honest and uphold the chivalric code, he accepts it out of the fear of death when he faces the Green Knight. Sir Gawain's decision to keep the green girdle instead of revealing it to his host (part of their agreement) ultimately becomes a key lesson in humility and honor in the poem.