Green tea has some caffeine.
And of course, caffeine can make tinnitus worse in sensitive people because it is a stimulant.
Before I stopped drinking caffeine due to migraines I never had T spikes from my morning cup of green tea, however. If you did personally experience spikes then I think it is best just to avoid caffeinated teas/drinks or limit the amount you drink(I understand that this would be quite challenging however)