In a medium saucepan, combine the chopped peaches, sugar, and 1/2 cup water. Bring to a simmer over medium heat, stirring occasionally. Reduce heat to low and cook for 10 minutes, until the peaches are soft and the liquid is syrupy and fragrant.

Remove from heat and let cool for 5 minutes. Pour the mixture through a fine-mesh strainer into a bowl, pressing gently on the solids with the back of a spoon to extract all the syrup. Discard the solids. Set the peach syrup aside.

In a separate saucepan, bring 4 cups of water to a rolling boil. Remove from heat, add the tea bags, and steep for exactly 5 minutes. Remove the tea bags and let the tea cool to room temperature, about 20 minutes. Do not squeeze the tea bags—this releases bitter tannins.

Fill a pitcher with ice cubes. Pour the cooled tea over the ice, then stir in the peach syrup to taste (start with half, then add more for a stronger peach flavor).

Serve immediately in tall glasses filled with ice. Garnish with fresh mint if desired.