1. Process raspberries in a blender or food processor until smooth, stopping to scrape down sides. Pour puree through a fine wire-mesh strainer into a large container, discarding raspberry seeds.
2. Bring sugar and 3 cups water to a boil in a saucepan, stirring often. Remove from heat; add tea bag. Cover and steep 5 minutes.
3. Remove tea bag with a slotted spoon, squeezing gently; cool tea mixture slightly. Stir together raspberry puree, tea mixture, grape juice, and lemon and lime slices. Cover and chill 2 to 24 hours. Stir in orange soft drink, and serve immediately over ice.
You can substitute 1 cup orange juice and 1 cup lemon-lime soft drink for orange soft drink.