Use your best judgment... I have had both happen to me. If the indoor temperature is cool, say 70 or so, the 2.5 - 3 week old tea should be ok. It would depend on how you prefer the tea though sweet-vinegar.
The black tea, hard to say without seeing it. I have had a dark grayish or bluish type of film around the culture on my greens and still used it as I did not believe it to be mold; so here, use your judgment.