.. How do I check on the item?

The authenticity database said if you shine an ultraviolet light on authentic ancient pottery, it reflects the light evenly; if it's been repaired, the different parts of the pottery shine differently.

There are black lights all over the place in the Underworld, but the only one you could look at closely was under Cerberus's foot.

When you look at it now, Nancy says she needs a wrench --

-- which you can now find in the Workshop, on the table on the right (where you got charcoal earlier).

Use the hex wrench on the blacklight, then use the blacklight on the pot in question; it's in the pottery display in the museum.

I'm not sure what Nancy sees that makes her so sure the vase is a fake, but let's take her word for it. After you use the blacklight, talk to Grigor, then Xenia, then Niobe in the Workshop --

-- whom you overhear having a tense discussion with Thanos. She then says she left you something on the stage, so go get it.

If you can't find it, stand on the lift door and look closely at the stone cylinders to the left; pick up one of the daffodils to get a key --

-- and take a quick unscheduled trip.

End Game: Trapped!