Add the flour, salt and cream of tartar to a medium mixing bowl.
Open 2 of the tea bags and pour the contents into the flour mixture.
Whisk to combine and set aside.
Microwave a cup of water until boiling.
Add the remaining 2 green tea bags and steep for 3-4 minutes.
Pour the hot tea into a saucepan or medium mixing bowl.
Add the vegetable oil to the hot tea mixture. Stir to mix.
Gently pour the flour mixture into the saucepan/bowl and stir continuously until a large lump of playdough forms.
Allow the dough to cool for 5 minutes before handling.
Transfer the playdough to a flat working space and knead for 3-4 minutes or until soft and pliable.
Store in an airtight container (or Ziploc bag) for up to 2 weeks.