We've had customers who tried all sorts of things in their moderators to reduce noise. Some people have used microfiber, foam, scotch bright pads and doubling up the felt are pretty common. Air needs to flow, so don't use plastics. One customer used MLV soundproofing barrier and reported good results on a Texan, so that might be worth looking into.
If, after trying other things you want to do a "factory reset" we offer replacement felt and screen
and have put together a tutorial on how to replace these parts in your moderator.
https://donnyfl.com/pages/felt-how-to?_pos=1&_sid=1e980a992&_ss=r