He doesn't hold it out for long before she snatches it back from him, giving the impression that there'd probably be trouble for him if he decided to withhold it from her for whatever reason. He doesn't, and she holds it tightly to her chest, not looking the least bit ashamed of her strange choice in accessories.

At the comment about the coat and mittens, she shakes her head, "It's important to me." She's lucky Eren hadn't given her a winter coat all those years ago or she'd probably be carrying that around instead.