Dished out pocketed snotrag - cheers! (5,3)

I believe the answer is:

thank you

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

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

(Other definitions for thank you that I've seen before include "I appreciate that" , "Ta" , "show appreciation" , "Much obliged!" , "Polite acknowledgment" .)

I've seen this clue in The Independent.

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