In a small saucepan, combine peaches, 1 cup water, and sugar. Simmer over medium heat for 15–20 minutes, stirring occasionally, until peaches are soft and fragrant. Lightly mash to release juices. Strain through a fine mesh sieve, pressing to extract as much liquid as possible. (Tip: Save the solids for oatmeal or yogurt!)
Brew the Green Tea:
Heat the remaining 3 cups of water until just below boiling. Steep green tea bags for 3 minutes, then remove and let cool slightly.
Combine:
In a pitcher, stir together green tea, peach syrup, and lemon juice. Taste and adjust sweetness if needed.