In a small saucepan, bring the water to a boil over medium-high heat. Turn off the heat, add the tea bags and let steep for 6 minutes. Remove the tea bags and cool the tea to room temperature, about 45 minutes. Pour the cooled tea into a large pitcher. Add the apple juice, Mint Simple Syrup and lemon juice. Refrigerate until ready to serve.
To serve, add the sparkling water and pour the punch into ice-filled glasses. Garnish with fresh mint sprigs, if desired.
Mint Simple Syrup:
Add the water and sugar to a small saucepan, and bring to a boil over medium heat, stirring occasionally, until the sugar has dissolved, about 3 minutes. Remove the pan from the heat and add the mint leaves. Allow the syrup to cool, about 20 minutes. Strain before using.