Combine sugar, 1 cup of water, and two peaches (pitted and chopped) in a small pot. Bring to a boil, then reduce heat and simmer, stirring occasionally, until the sugar is dissolved, about 6 minutes.
Remove mixture from heat and let sit 30 minutes. Then strain mixture through a fine-mesh sieve into a large pitcher.
Bring 6 cups water to a boil; remove from heat. Steep tea bags in the hot water for 10 minutes.
Carefully pour tea into pitcher with the peach syrup and refrigerate until chilled.
Pit and thinly slice the remaining peach.
Serve on ice, garnished with peach slices.