How can I remove old tea stain from carpet/rug?
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.