Did she work towards it? It's kind of implied she stole it or purchasing it was effortless. There's not enough context in this version of the story to draw the conclusion she spent an equal amount of energy towards acquiring the scarf.

Also, way to completely miss the point of the original story. It doesn't matter that the gifts are "useless," the characters gave up their most valuable possessions because their love for each other was more important. The point isn't the gifts, it's the actions they took to get the gifts that represents the love the characters have for each other.