In the late 1700s and throughout the 1800s, twankay or twankey was used to refer to the lowest quality of green tea, described as having an old, ragged, and open leaf. This appears to be from a corruption of Tunxi District in China.
Today you will sometimes see Tun Xi Lu Cha (lit. Tunxi green tea) marketed as twankay, even high-end Tun Xi Lu Cha. However, this does not refer to the grade, but the source and type of tea. This tea might also be called Tunlu or Tunlü.
These days, if you hear the term twankay outside of a teashop, it's probably a reference to Widow Twankey of the popular Aladdin pantomime.