Bring 3 cups (750ml) water and the sugar to a boil in a pot. Add the peaches and vanilla bean (including the seeds). Simmer over medium heat for about 30 minutes.
Discard the vanilla bean. Pour the peaches and syrup into a blender and puree until smooth. Strain the peach puree through a sieve into a pitcher.
Bring 4 cups (1 liter) water to a boil in a small saucepan. Remove from the heat, add the tea and steep according to the package directions. Strain to remove the tea leaves, then add the tea to the pitcher with the peach puree. Stir to combine. Refrigerate until cold.
The pulp from the fruit may have separated from the tea during chilling, so be sure to stir it before serving. Pour over ice cubes in tall glasses and garnish with vanilla beans.
When blending hot liquids, remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.