The wire cage that holds a sparkling wine cork onto the neck of the bottle is called a:

D.

Known in French as a muselet or muzzle, the wire cage that holds a Champagne or sparkling wine cork in place is very important in opening a bottle of bubbly safely. The muzzle should not be removed before the cork is eased out. Rather, the muzzle should be loosened (about 6 turns will loosen it), and then the wire removed with the cork at the same time.