1. Combine sugar and three-quarters of a cup of water in a medium saucepan over medium heat. Bring to a boil and cook until the sugar dissolves, about four minutes.
2. Reduce heat and add tea bags. Let simmer on a low flame, allowing the tea bags to steep for 15 minutes. Discard tea bags.
3. Place cubed honeydew in a blender along with the remaining half cup of water. Blend well. Push blended honeydew through a sieve into a 9×13-inch pan.
4. Add the lemon-flavored syrup into the pan along with honeydew. Mix well.
5. Freeze for at least eight hours. When ready to serve, scrape iced honeydew with a fork until you have small ice crystals. Place one cup of honeydew crystals into a tall glass and top with half a cup of seltzer.