Use some Goof-off or Goo-Gone with some lightweight fishing line. Dental floss works pretty well too if you double or triple it up. Spray a little bit ofo the gunk removing around the badge and let it soak in for a bit. Try to avoid spraying it everywhere as it can't be overly good for the paint. After a little bit, start with the fishing line and gently saw back and forth behind the badge. There are a couple of pins so you aren't going to be able to go all the way through. Once you've got both sides you can slowly pull the badge off. Once off, clean the surface of any remaining glue and you're ready to put the new on one. Just be sure to use some sort of automotive glue or it will fall right off. The stuff I used can be found at Walmart and it intended for automotive exterior trim.
