Working in batches, puree 6 cups cubed honeydew melon in a blender. Pour puree through a fine sieve into an 8-inch square nonreactive dish.
Put 1/2 cup water and sugar into a small saucepan. Bring to a boil over medium-high heat, stirring until sugar has dissolved. Stir into puree. Add fresh lime juice; stir to combine. Freeze, covered, at least 6 hours (up to 3 days).
Scrape granita with a fork; spoon about 1 cup granita into each of 6 glasses. Pour 1/2 cup seltzer into each glass; garnish with lime peels.