I've just removed mine, but yes, you have to sand the whole coating off... the logos are just the original black plastic showing through.
I started with 150 grit sand paper to get the rubbery stuff off, then moved onto 600 (or 800?) grit wet & dry paper to remove most of the scratches before it was ready for primer.
Few coats of primer, sand it down, another coat if necessary, sand again if needed, then paint with your chosen colour!
Doesn't take long really, although you do need to be vigilant and sand right into all of the corners to ensure its all off before painting!