Peel and section grapefruit; set sections aside. Reserve rind from 3 grapefruit. Cut pith from rind, and discard. Cut rind into thin strips.
Cover rind with water in a saucepan; bring to a boil, and boil 5 minutes. Drain and return rind to saucepan. Stir in 1 cup sugar, grenadine, and corn syrup.
Cook over medium heat, stirring constantly, until a candy thermometer registers hard crack (300°). Drain rind quickly, and toss with remaining 3/4 cup sugar. Let pieces cool on wax paper; store in airtight container.
Stir together ginger ale, Campari, and ginger. Pour over grapefruit sections. Cover and chill at least 2 hours. Serve with candied rind.
*2 (24-ounce) jars grapefruit sections may be substituted for fresh. If using