The other day while taking notes during a conference call I accidentally wrote on my whiteboard with a Sharpie marker. After several minutes of swearing I remembered a tip I had heard years ago.
Using a white board marker scribble over the permanent marker and wait a few minutes. 
With the dry whiteboard eraser wipe off the dry erase and the permanent marks come with it. It may take a couple of tries but you should be able to get rid of almost all of the permanent marks.
I’m not sure why the dry erase ink causes the permanent ink to release but I’m certainly glad that it does!