Put the strawberries, 2 tablespoons of the sugar, the lemon juice, and the salt in a food processor or blender. Process until it's a smooth puree, pour it into a container, and refrigerate until needed.

In a small saucepan, bring the 2-1/4 cups water to a gentle boil. Add the tea bags, remove from the heat, cover, and steep for 15 minutes.

Pour the remaining 1/2 cup sugar into a 3-quart heatproof container (like a large Pyrex liquid measure). Remove the tea bags when they're finished steeping (don't squeeze them) and pour the tea over the sugar, stirring to dissolve the sugar. Add the 6 cups cold water and stir again. Chill until cold.

To serve, combine the strawberry puree with the mint tea and stir well to mix completely.

If serving in a punch bowl, put the strawberry-mint tea in the punch bowl and slowly add the sparkling water. For individual servings, fill 10-ounce stemmed glasses (wineglasses work great) two-thirds of the way with the tea and top off with the sparkling water. Garnish with mint sprigs and a strawberry, if you like.