Mix 1 cup water, sugar, and peach slices together in a saucepan; bring to a boil. Reduce heat to medium and simmer, crushing peach slices as you stir, until sugar is dissolved, about 5 minutes. Remove saucepan from heat, cover, and allow peaches to infuse syrup, about 30 minutes. Strain to remove peach slices.
Bring 6 cups remaining water to a boil in a separate pot. Remove from heat, add tea bags, cover, and steep for about 5 minutes.
Remove tea bags from the pot, pour in peach syrup, and cool to room temperature. Refrigerate until ready to serve.