Make an aromatic simple syrup by boiling the tea with the sugar and spices until the sugar is dissolved. Strain and cool.
Brush some of the syrup over salmon fillets half an hour before grilling, reserving some for serving.
Grill over medium heat until the flesh of the fish just begins to flake, about 7 minutes. It should yield slightly to the touch. Flip over after establishing nice grill marks, about halfway through. Top with some more syrup just before removing from the grill.