Bring 4 cups water to a boil, add the tea bags and lime peel. Remove from the heat, and let stand for 5 minutes. Remove the bags and peel, then transfer the tea to a pitcher and chill.
Put the diced sugar, chopped lime and mint leaves in a pitcher and muddle. Stir in the chilled tea, rum and lime juice. Sweeten with the simple syrup. Pour over ice into 4 tall glasses, and then garnish each glass with a mint spring.