Place tea bags in a large heatproof bowl. Pour over 4 cups of boiling water. Stand for 1 hour, then remove tea bags, squeezing out excess liquid. Discard tea bags. Stir in lime cordial and pineapple juice, refrigerate until cold.
Using a melon baller, cut balls from the melons.
Just before serving, combine tea mixture, lemonade and melon balls in a large serving jug. Decorate with lime and mint.