matte = dull = not polished.
It's as simple as that.
WHat I'd suggest is sanding it down to 180 or 220 grit. Use a device or procedure to remove the oil (Columbia's CPR system, Ebonite's Hook Again system, the Rejuvenator heating system, or the hot water + Dawn system). Then resand it back up to 1000 grit, using any sanding system you desire (wet/dry sandpaper, Scotch-Brite nylon pads or Abralon pads): 180, 220, 320, 400, 600, 800, 1000 grit. Use lots of water in the sanding part.
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"...for advice is a dangerous gift, even from the wise to the wise...."
J. R. R. Tolkien