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I had a similar problem. Mine were so clogged that virtually no air would pass through the wire screen. I could not find a way to remove the wire screen.
This may not be the best way, but it worked for me.
1) Vacuumed the screen using an upholstery brush attachment to remove as much dirt as possible.
2) Sprayed out the screen with compressed air. This sent a lot of dirt out of the side vents.
3) Used a small amount of CRC brand Mass Air Flow cleaner spray to clean the wire screen. I happened to have a can on hand and it works well to clean fine wires without leaving a residue.
I ended up bending it out the slotted housing but it broke in half so only the bottom half has a screen and the top is wide open. If i get the proper name of the part maybe i will order one. Until then i am enjoying my center vents blowing strong again.