This booze-free cocktail gets its green tint from honeydew melon balls. (A little gin will give this an alcoholic kick.)
Cut honeydew in half and remove seeds. With a melon baller, scoop out 24 melon balls and reserve in refrigerator. Remove rind from remaining honeydew, and cut the melon into 1/4-inch pieces. You should have about 8 cups of fruit.
In batches, pulse fruit in blender on low speed until small pieces remain, about 30 seconds. Strain through a sieve, pushing on melon with the back of a spoon or ladle, to yield about 3 cups juice. Discard remaining melon.
Bring 1/4 cup water and the sugar to a boil in a small saucepan. Add tea, and steep for 3 minutes; strain and chill in refrigerator.
Fill six 12-ounce glasses with ice and 4 melon balls each. Mix honeydew juice, jasmine-tea syrup, and seltzer; divide among glasses. Stir and serve immediately.