Make the matcha yogurt: In a 4-cup liquid measuring cup, combine the water and matcha, and whisk vigorously to dissolve. Stir in the honey and milk, and add the yogurt last. Refrigerate until ready to use.
Make the raspberry puree: Prepare an ice bath. In a covered medium saucepan over high heat, bring the raspberries, honey and water to a boil. Remove the lid and continue to cook at a low boil, stirring often, until the berries fall apart and the liquid reduced to a syrup, 3 to 4 minutes. Remove from the heat and pour into a small bowl set over the ice bath. Let cool completely.
Assemble the ice pops: In each ice pop mold, alternate the layers, adding 3 tablespoons of the matcha base and 1 tablespoon of the raspberry compote, to create a marbling effect. Insert sticks and freeze until solid, 5 to 6 hours.
Unmold the ice pop by dipping each mold into warm water for 10 to 15 seconds. Serve immediately.