Don't really know how I managed to do it, but I scratched a small section of my clear bra with a microfiber towel. Looks frosted, like my iPod screen.

Any thoughts on how to remove them?

 

plastic polish on foam applicator should take care of it. go slow and
moderate pressure. make sure the surface does not heat up from
friction.

clearbra swirls VERY easily. even taking your dry finger tips accross it
will swirl it.

wax afterwards. wax does a great job hiding clearbra swirls.