Combine cherries and ginger slices in a glass bowl.
Sprinkle sugar over the cherries mixture and cover with 2 cups filtered water.
Cover bowl with plastic wrap and refrigerate 2 hours to overnight.
Bring 2 cups filtered water nearly to a boil; pour over tea bags in a pitcher. Steep tea for 90 seconds. Squeeze tea bags into pitcher and discard bags.
Strain cherry-ginger water into pitcher with green tea, squeezing out excess liquid.