Heat the water to 75–80°C (167–176°F), do not boil. Add the green tea bags and steep for 2–3 minutes maximum. Remove the tea bags without squeezing and let the tea cool to lukewarm.
Add the lime peel strips to the warm tea. Let infuse for 5–8 minutes only, just until a pronounced lime aroma develops. Remove the peel promptly to prevent bitterness.
Once the tea has cooled to room temperature, stir in 1 tablespoon of lime juice. Taste and add up to 1 additional tablespoon only if needed. The acidity should be light and refreshing, not sharp.
Refrigerate for 1–2 hours until fully cold and crisp.
Fill glasses with ice, pour over the chilled lime green iced tea, and garnish lightly with lime peel or a thin slice if desired.