Crossword Genius

Cutback means couple must abandon re-education (9)

Ross

I believe the answer is:

reduction

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

'couple must abandon re-education' is the wordplay.
I cannot quite understand how this works, but
're' is found in the answer.
This explanation may well be incorrect...

'means' is the link.

Can you help me to learn more?

(Other definitions for reduction that I've seen before include "from nine to five, for example" , "Decrease, diminution" , "cutback!" , "Introduce by way of discount" , "Lessening" .)

I've seen this clue in the Sydney Morning Herald.
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