Prepare the tea: Boil 1 cup of water and pour over the 4 tea bags. Steep for 5-7 minutes for a strong brew. Discard the tea bags, and stir in 3 cups of cold water and ice until the tea is completely chilled.

Prepare the raspberry syrup base: In a small saucepan, combine the frozen raspberries and simple syrup. Heat gently over medium-low heat until the raspberries begin to soften and release their juices (about 3 minutes). Mash slightly with a fork.

Combine the fruit flavors: Pour the raspberry syrup mixture (straining is optional, but recommended for a smoother texture) and the peach puree into a large pitcher. Add the fresh lemon juice and stir to combine thoroughly.

Mix the beverage: Pour the chilled, strongly brewed iced tea into the pitcher with the fruit mixture. Stir well until everything is completely incorporated and the color is uniform. Taste and adjust sweetness if necessary.

Serve immediately over plenty of ice. Garnish each glass with a peach slice resting on the rim and a few fresh raspberries floating on top.