Run a piece of floss behind the badge to separate it from the foam adhesive pad.

Peel off the left over foam adhesive. If it doesn't peel up easily, soak it with some Goo Gone for a few minutes.

Using Goo Gone, wipe off the leftover adhesive. I like to alternate between alcohol and Goo Gone until the adhesive is gone.

Use some wax and grease remover to remove any of the Goo Gone that might be left over. The surface should be completely clean, but may still show a slight outline of the badge. This is simply because the paint that was underneath the badge was protected from the elements until now.

(Optional) Install a new badge by peeling off the backing paper and carefully aligning it before pressing it onto the car.