Bring 6 cups water to a boil in a large saucepan. Remove from the heat, add the tea bags and let steep 8 minutes. Discard the tea bags. Pour the tea into a small pitcher and refrigerate at least 1 hour.
Meanwhile, bring 2/3 cup water, the sugar and lemon thyme to a simmer in a medium saucepan over medium heat. Cook, stirring, until the sugar dissolves. Let cool, then strain into a liquid measuring cup. Refrigerate at least 1 hour.
Puree the peach in a blender with the tea, lemon thyme syrup and lemon juice until very smooth, about 1 minute. Strain through a fine-mesh sieve into a pitcher and stir in the gin. Refrigerate until ready to serve. Stir and divide among mason jars filled with ice. Garnish with lemon slices.