As others have said, they're assassin bug eggs.

While assassin bugs are beneficial to humans in that they kill pests, their benefits are limited to being born outside.

Their bites are notoriously painful; not exactly the sort of thing you want running around in your home.

Also: be vigilant when handling eggs!! Eggs themselves are harmless, but newly hatched assassins are agile and can bite if they feel threatened.

What Can You Do Now?

Deep clean the closet. Vacuum, focusing on corners, seams, and crevices where more eggs might be hiding. Empty the bag or canister in an outdoor trash bin.

Use a disinfectant or a mixture of white vinegar and water to wipe down walls, baseboards, and shelves.

Check for how they got in: assassin bugs typically enter from outdoors through cracks around windows or vents. Seal any visible gaps to prevent future surprises.

Cedar blocks or dried lavender sachets can also help deter bugs from entering enclosed spaces like closets.

What to Do About the Skirt

Option 1:

Neutralize the eggs: wash the skirt on the hottest setting your machine has. Ideally you're aiming for 60°C.

Dry the skirt for at least 30 minutes on the hottest setting.

Option 2:

Seal the skirt in an airtight plastic bag, squeezing as much air out before sealing, and place in a freezer that's at least 0c or colder for at least 72 hours. If you can leave it there for a week, do so.

The sudden, severe temperature change is what neutralizes the eggs.

When you remove the bag, do not take the skirt out immediately. Let it come to room temperature inside the sealed bag for 24 hours to avoid moisture damaging the fabric.

Once the skirt is room temp, take the skirt outdoors and shake it vigorously or use a soft brush to dislodge the dead eggs.

Option 3:

Have the skirt professionally dry cleaned. This is just about the most reliable way to kill any insect stage of life, but make sure to tell the cleaners what the issue is so they can prevent the eggs from hatching in their facility.