To brew the tea: Pour the boiling water over the tea bags; let steep until cooled. Squeeze out tea bags.

To make the blueberry simple syrup: Place blueberries, sugar, and 1 cup water in a small saucepan over medium-high heat. Bring to a boil; reduce heat and simmer for about a minute. Remove from heat and let cool. Once cooled a bit, strain the syrup to remove the blueberries. Mash the blueberries against the side of the strainer to release all of their juice, letting this juice strain into your simple syrup. Squeeze in the lime juice; stir to combine.

Combine the brewed tea and blueberry simple syrup in a 2-quart pitcher. Fill the remainder of the pitcher with cold water to make 2 quarts. Serve over ice with a lime wedge.