Add the sugar and the water together in a medium saucepan over medium-low heat. Stir until the sugar is completely dissolved.
Add the blackberries and cook for 10 to 15 minutes or until the syrup has become the color of the fruit and the fruit has lost its vibrancy.
Add the vinegar and bring the mixture back to a simmer (about 5 to 8 minutes). Turn off the heat and add the tea leaves, letting them steep for 3 minutes.
Strain the fruit and the leaves out using a fine-meshed sieve covered with one layer of cheesecloth.
Pour into a jar and keep it in the fridge.