To remove dry tea stains from carpet or upholstery, try mixing two cups of cool water with one tablespoon of dish washing liquid and one tablespoon of white vinegar. Using a clean white cloth, apply this mixture to the stain and blot until the stain lifts. Afterwards, blot dry.
Another option is to use a carpet stain remover. Follow the usage instructions of the product closely, as it may damage the carpet if not applied correctly. It is also a good idea to test both the mixture above and carpet stain remover on a hidden area of your carpet as both may have a bleaching effect.