'Dregs' is, on the contrary, particularly the tea material, the solid part or sediment -- though the term is often used for whatever is not used (= liquid + solid). However, I believe that they just as often remain tea leaves, as in this excerpt about tasseography: After a cup of tea has been poured, without using a tea strainer, the tea is drunk or poured away. The cup should then be shaken well and any remaining liquid drained off in the saucer.
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hrsaneiThanks Mister Micaber,So we have to use tea strainer to avoid tea leaves in our cup.