Tees full of booze after sending back a puzzle (6)

I believe the answer is:

enigma

I'm a little stuck... Click here to teach me more about this clue!

'puzzle' is the definition.
(I've seen this before)

I don't understand how the remainder of the clue works.

(Other definitions for enigma that I've seen before include "It's mysterious like gamine" , "cryptic puzzle!" , "German military cipher machine" , "Mysterious puzzle" , "WWII cipher" .)

I've seen this clue in The Independent.

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