Heat the water. Bring 3 cups of water to a gentle boil.
Keep the remaining 1 cup cold for later.
Steep the tea. Add tea bags to a heatproof pitcher or saucepan. Pour over the hot water and steep for 3–4 minutes. Avoid oversteeping to prevent bitterness.
Sweeten while warm. Remove tea bags.
Stir in honey or simple syrup until dissolved. Start with 2 tablespoons; you can adjust later.
Mash the raspberries. In a separate bowl, lightly mash the raspberries with a fork to release juices but keep some texture. If using frozen raspberries, thaw first for better flavor release.
Combine and dilute. Add the mashed raspberries, lemon juice, and the remaining 1 cup of cold water to the warm tea.
Stir well.
Chill. Refrigerate for at least 1–2 hours so the flavors meld and the tea cools completely.
Strain (optional). For a clearer drink, strain through a fine-mesh sieve to remove most seeds and pulp. If you enjoy texture, skip this step.
Taste and adjust. Check sweetness and tartness. Add a touch more honey or a squeeze of lemon if needed.
Serve. Fill glasses with ice.
Pour the raspberry iced tea over the ice. Garnish with mint, lemon slices, or a few fresh raspberries if you like.