Usually, you could grill a fish filet like this with the skin on (salmon, for instance), but carp have what is known as a "mud vein" just under the skin which is nice to remove. You will have to skin them to get to it.
With the meat-side up, start cutting gently along the width at one end of the filet until you can lay your knife sideways in the slit. Carve with pressure towards the cutting board, in long strokes the length of the knife. Hold the skin back with your non-dominant hand.
