Head scratched in difficult argument (4)

I believe the answer is:

tiff

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'argument' is the definition.
(I know that tiff is a type of dustup)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for tiff that I've seen before include "Row; argument" , "Petty squabble" , "Mild quarrel" , "Hard to lose opening argument" , "A spat or small row" .)

I've seen this clue in The Times.

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