Boil 3 cups of water in a saucepan. Remove from heat and place tea bags in water and let steep for 25 minutes
While tea is steeping, add cubed peaches, 2 1/4 cups of water, and white sugar in a large saucepan and stir together. Bring mixture to a boil, reduce heat to low, cover and simmer for about 15 minutes or until peaches are very soft
Mash peaches using potato masher. Continue simmering covered for 10 more minutes
Strain peaches through a fine mesh strainer over a large bowl or container and discard solids
Remove tea bags from water and discard. Pour tea into large pitcher. Mix peach syrup into tea. Add about 4 cups of additional water to pitcher and stir. Refrigerate until cold
Serve over ice. Garnish with fresh mint and peach slices if desired