going backwards, wood filer will work on that engraving. No problem there.
The stimulating question of yours is the removal of that vinyl or paper vineer over the particle wood. I would try to pick a piece of vineer and try to pull it off, may take many pieces. I would not consider sanding it because I think it would gum up badly. I am assuming that this is not a hard vineer laminate, if so, you can easily pull this off.