Bring 2 cups (500ml) water to a boil in a medium saucepan. Add tea bags and ginger. Cover and steep for 5 minutes. Remove and discard tea bags and ginger, squeezing bags gently to release excess water. Stir in honey until dissolved. Pour mixture into serving jug.
Place ice in a 4-cup (946ml) measuring cup and fill with water to 3 cup mark. Add to jug with lemon and lime juice, stirring to combine. Garnish with lemon and lime slices and serve.