How to remove carpet tape from flooring

Sorry to hear about your stain, but here are two options.

Tea should be fairly easy to remove. You can try blotting it out with very hot water and an absorbent cloth, or borrow a carpet cleaning steam machine and give it a try. Another option would be to hire a commercial carpet cleaning service. I use this type of service all the time in the apartments I manage. In this area it only costs me about $80 per room and the results are amazing. If you talk with a cleaning service, they can tell you if your stain can be removed before you hire them. Some will guarantee that the stain will be gone. This option is certainly a lot cheaper than paying to replace the entire carpet and padding. Good Luck.

Depending on when this happened you might be able to just use water, or soap and water. Before it cures, latex paint is water soluble (so the absolute best time to clean it up is before it dries at all). I've had good luck using a couple of sponges and warm water - one to apply fresh clean water to the paint, and the other to blot up dissolved paint/water. You can continue this until the spot is gone.

If the paint is cured (i.e. the water isn't breaking it down) then there is a cleaner called "Oops!" that works well on paint, ink, tar etc on carpets. I would try some of that as I've heard it works wonders. It should be available at your local hardware store.