Brew the tea by boiling 4 cups of water. Remove from heat, add tea bags, steep for 5 minutes, then remove bags and let cool.
Blend the chopped mangoes until smooth, then press the puree through a fine-mesh sieve into a bowl.
Simmer the sugar and 1/4 cup water in a small saucepan until the sugar dissolves completely to make a simple syrup.
Mix the cooled tea, mango puree, simple syrup, lemon juice, and 2 cups of cold water in a large pitcher.
Chill the pitcher in the refrigerator for at least 2 hours before stirring well and serving over ice.