I use some stuff called "Goo Gone" and a small hypodermic needle like diabetics use.
Fill the hypodermic needle with Goo Gone, slide the needle behind the glue strip along the top edge as close to the body as possible to get between the glue and the foam tape. Inject some Goo Gone then walk the needle along the same edge to start loosening the glue.
Repeat several times. After the first injection, I can usually slide dental floss behind the badge and open the "crack" a bit more to squirt more goo gone and let it work.. the goo gone doesn't attack paint or plastic.. only the glue.
With a bit of work.. you should have a clean removal with no damage. Use the reverse to take the remaining tape off the back side of the badge. Hot soapy water removes the Goo Gone residue. Let everything dry and apply new tape to replace the badge.