It depends on what he used. If it's shellac, denatured alcohol will remove it. You might want to test the alcohol on the MB-tex to see how careful you need to be. I would use cotton balls and work in a small area.
If it's lacquer or polyurethane, it's very difficult to dissolve. I wouldn't attempt to refinish it without removing it from the dash.
Whatever you do, do not use anything abrasive like sandpaper or steel wool. The veneer is very thin and easy to sand through.
As for new finish, the options are many depending on what you want. You can do an oil finish with the wood in place, but you'll have to be very careful to keep it off the Tex. Personally, I wouldn't try it. The PO of my car got some sort of finish all over the dash, if I'm going to get rid of the stains I'll need to recover the dash.