Bring 3 cups of water to a boil in a medium saucepan. Add the tea bags, remove from the heat, and let steep for 8 minutes. Remove the tea bags and stir in the agave nectar or honey. Pour the tea into a pitcher and chill until cold, at least 1 hour.
Meanwhile, puree the watermelon and mint in a blender or food processor. Run the puree through a medium-mesh strainer, pressing on the pulp to extract the juice. Discard the pulp.
Stir the watermelon juice and lime juice into the chilled tea mixture. Pour each serving over ice and garnish with a mint sprig.
Tip: For sweeter iced tea, stir in more agave nectar or honey just before serving. For caffeinated iced tea, use a mixture of black tea and peppermint tea bags.