Fill a medium sized saucepan with the water. Add the tea bags and over medium-high heat, bring the water to a boil. Just as the brew comes to a rolling boil, turn off the heat and cover for 5 minutes. Remove the tea bags.
Add the sugar and zest stips. Stir until sugar is dissolved.
Allow the mixture to cool.
Remove the lime zest and pour into a pitcher. Stir in the fresh lime juice.