How do I get lint off a silk duvet cover?

I’ve just taken my silk duvet cover out of the wash and it is covered in lint. How do I get the lint off? It’s currently hanging up to dry.

(I am, of course, cleaning the washing machine.)

Use one of those sticky-tape lint roller things? Or, if you don’t have one, wrap several turns of Scotch tape, sticky side out, around your hands and pat down the duvet.

Should I wait until the duvet cover is dry?

I fear I have damaged the silk somehow. There are areas which are visibly furry - no lint, but fibres above the surface.