Put the tea bag in a cup, pour over the boiling water, and leave to steep for 5 minutes. Remove the tea bag and let cool completely.
Remove the pips from the melon, cut away the peel, and chop the flesh into chucks. Put the melon and pineapple in a food processor or blender and blend until smooth. Strain through a sieve to remove any hairy pulp.
Dilute the fruit pure’e with 3 tablespoons of the cooled tea, then pour into a glass filled with ice cubes and serve immediately.