Bring water to a boil. Add tea, lemon rind, and mint. Remove from heat and steep 5 minutes.
After steeping, strain out solids in a colander or coarse mesh strainer, but do not discard solids yet. Add sugar to hot tea and stir to dissolve.
Run cold water into the tea through the strained solids, squeezing rinds and tea solids to release juices.
Add lemon juice and pineapple juice to cooled tea and mix. Transfer tea to storage container, straining again, this time with a fine mesh strainer.
Dilute to taste. This recipe makes about 1 gallon of undiluted tea or up to 2 gallons fully diluted (if you like it that way.) Can store it undiluted and just add a little water to the glass when serving.