Boil water.
Hang tea bags in a heat-resistant container, pour the boiling water on them, let them steep for 2 minutes and then remove the tea bags.
Put ice cubes in a water carafe and pour the hot tea over it.
Cut honeydew melon in half and remove seeds.
Using a melon corer or ice cream scoop, pry out a few balls of pulp from the honeydew halves and divide the melon balls among drinking glasses.
Loosen the remaining honeydew pulp from the rind and cut it into rough pieces.
Place the honeydew pieces, mint leaves, and lime juice in a blender and puree until fine.
Pour the honeydew mixture to the white tea in the water carafe and stir it.
Add ice cubes to the melon balls in the drinking glasses and pour the honeydew iced tea over them.
Serve the honeydew iced tea with fresh mint leaves.