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.
In a small saucepan, combine the strawberries, sugar, and water. Bring to a gentle simmer over medium-low heat and cook for 8–10 minutes, just until the strawberries soften and release their juice. Do not reduce aggressively or let it turn jammy. Remove from heat.
Strain the syrup through a fine-mesh sieve into a bowl or measuring jug. Do not press the solids. Discard the strawberries and let the syrup cool completely.
While the tea is still slightly warm, stir in 100–140 ml of the cooled strawberry syrup. Taste and adjust carefully — the strawberry should be light and supportive, not dominant.
Stir in 1 tablespoon honey to round the acidity and fruit. Taste and add up to 1 additional tablespoon only if needed. The goal is balance, not sweetness.
Rinse the lemon balm leaves and gently clap them between your hands to release aroma. Do not chop or bruise aggressively — lemon balm is delicate and turns grassy fast.
Add the lemon balm leaves to the cooled tea. Refrigerate and let infuse for 6–10 minutes only, just until a clean, lemony herbal aroma develops. Remove the leaves promptly to avoid bitterness.
Continue chilling the tea for 1–2 hours until fully cold and integrated.
Fill glasses with ice, pour over the chilled lemon balm strawberry green iced tea, and garnish with fresh lemon balm leaves and strawberry slices.