Hi, Greg,
Pick up clear Ammonia 79 cents/QT from a grocery store, soak the badge in. May be 30 minutes or so. The green stuff will melt away. Do not sand or buff, you loose too much brass material on the base metal (it could be solid copper).
Take a photo in close up before you do anything, so you always can review the original looks. Probalbly the old paint peel away while you are soaking the badge.
Happy Holidays!
KEN TODA, High Point, NC, windy but beautiful Carolina Blue sky.