Did you get it right?
One modern fastener appears among period sewing items.

The Answer
The correct answer is: the modern plastic snap-hook garment clip.
Here is why
- The robes, hangers, thread, buttons, and pins fit the room.
- The plastic snap-hook is the odd modern item.
Why people miss it
It is small enough to blend into the robe room at first glance.
What answer did you get before checking?