Heat the water to 90–95°C (195–203°F). Add the black tea bags and steep for 2½–3 minutes maximum. Remove the tea bags without squeezing and let the tea cool to lukewarm.
Rinse the thyme sprigs and gently clap them between your hands to release aroma. Do not chop or bruise aggressively — thyme turns heavy and medicinal fast.
Add the thyme sprigs to the cooled tea. Refrigerate and let infuse for 6–10 minutes only, just until a fresh, green herbal aroma develops. Remove the thyme promptly to avoid bitterness.
Add the orange peel strips and let infuse for 5 minutes, then remove. Stir in ¾ cup fresh orange juice and taste, adding up to 1 cup total only if needed. The juice should gently sweeten and brighten, not dominate.
Continue chilling the tea for 1–2 hours until fully cold and balanced.
Fill glasses with ice, pour over the chilled thyme orange iced tea, and garnish with fresh thyme sprigs and orange wedges.