Pieces are not flat!

Removed the poor felt ,found the bottoms are really bad!

Metal appears,above the bottoms the pieces.
How to get the weight out ? 
Need re-fit!

i have used sand paper before and dremel to grind away metal that was sticking out and making chess pieces woble.

If it is lead, you can sand it off with a 100 or 200 grit sandpaper. If it sticks out a lot, some of it can be cut off sliver by sliver with an utility knife. (If not lead, you may need to use a flat file.) Fix sandpaper on table with tape, then drag a piece by piece over it, moving the pieces, NOT the sandpaper. This will help against sanding off the edges. Takes some elbow grease, but can be done. Just be sure to keep bottoms flat against sandpaper.

Same with a file, clamp it into a vise. Do not try the other way around, you will ruin the pieces.

-Izmet Fekali

Is it wise to wear a dust mask if using a dremel to grind lead?

Izmets advise is the best. 

I all walks of life a felt bottom is pleasure.