In a medium saucepan, boil the water, remove from heat, and steep the tea bags for 10-15 minutes.
Remove the tea bags and set aside - you will be using them again!
Add flour, salt, cream of tartar, and oil to the saucepan and stir continuously over medium heat. The dough will thicken and eventually form a ball.
As soon as it forms a ball, remove from heat and stir in the contents of 2-4 of the tea bags.
Remove the playdough from the saucepan (I like to use a wooden spoon) and place in container that can be sealed. However, wait until the dough has cooled before sealing. (Usually, I wait until the dough has cooled just a bit and then hand it over to my kids to play with warm. By the time they are finished, it is completely cooled and able to be put away in a plastic container with lid.)