There is a product which is a tea bag that works in cold water. Can it be steeped in shabbas if the tea bag is left in the pitcher? It seems questionable or careful a good plan.
It can be steeped on Shabbos, however it is preferred to put the tea bag into the cup or container before adding the water. If the tea bag was put into the water it is still permitted, however it is better to pour the water on to it than to put it into the water itself.
According to most poskim we say “aiyn tzeviah bochlin” dying doesn’t apply to foods, when the purpose is not to color the water but only to add taste. See O:CH 320-19, M:B 320-56. However being that there are opinions that it does apply there is a preferance to add the “color” before the water, but if it wasn’t done it is still permitted.