Grasp a thick marker using your normal pencil grip (the thickness of the marker will make repositioning your grip easier than with a thin pencil). Move your fingers so that your index and middle finger are gripping the front of the marker and your thumb is holding the back.
Write with the marker on a piece of paper, making sure to maintain the finger placement. Continue writing with the marker until you can firmly hold the marker in the correct position and the grip feels less awkward to you.
Replace the thick marker with a pencil, place your fingers back into the same position and write on a piece of paper again. Watch your hand as you write, and observe if your knuckles turn white or it appears you are pushing down too hard (for example, if you frequently break the pencil's lead). If so, crumple up a paper towel as small as possible and place it into your palm before gripping the pencil; this will help you loosen your overly tight grip and realize how your hand should be positioned.
Practice writing slowly with the correct grip on a daily basis, even if you can only devote five minutes. Consistency can help you toward a permanent change in pencil grip.