1. Bring 2 cups water to a boil in a medium saucepan. Stir in tea; cover and steep 5 minutes.
2. Place sugar in a pitcher. Pour warm tea through a sieve over sugar, stirring until sugar dissolves. Discard tea leaves. Cool completely.
3. Stir pomegranate juice and ginger syrup into tea mixture; cover and refrigerate until thoroughly chilled.
4. Fill each of 4 glasses with ice. Pour 2/3 cup tea mixture over ice in each glass; add 1/2 cup sparkling water to each glass. Garnish with lime slices, if desired.