Describe the special characteristic of the gift which Gawain keeps secret from his host.

He has a girdle that supposedly protects him.

It was given to him by the Knight's wife.

The host's wife gifts Gawain with a green sash and tells him that the knight who “bears it knotted about him” cannot be defeated by any man or any magic." He of course accepts based on the sash's powers, and also agrees to keep it a secret from her husband so he can use it at the Green Chapel.

Yes, she gives him a sash as well to protect him.