For the tea, in a small saucepan over medium heat, combine the flowers, water, and sugar. Cover with a lid and bring to a boil. Remove from heat and let it steep for 15 minutes.
Meanwhile, prepare the simple syrup. In another small saucepan over medium heat, combine the water and sugar. Bring to a simmer and the sugar has melted. Remove from heat and let it cool to room temperature.
Back to the tea, strain the tea through a fine mesh sieve into a glass bowl. Discard the flowers. Let the tea cool to room temperature, about 45 minutes.
For the juice, in a blender, combine the strawberries, cold water and ½ cup plus 2 tablespoons syrup. Blend until smooth. Strain the juice through a fine mesh sieve to a medium bowl. Discard the seed. Combine the juice and tea. Taste and adjust with more simple syrup if needed.
Fill the popsicle molds with the strawberry mixture. If using molds that contain sticks or hold wooden ones in place, put on lids and freeze. If using open cup molds, freeze until beginning to set, about 1½ hours, then insert the sticks and put back in freezer.
After about 8 hours, popsicles are ready. If the popsicles are stuck in the molds, dip the molds in warm water for 10 seconds or so. Remove molds and serve.