Change for the better? - Crossword Clue, Answer and Explanation

'change for the better?' is the definition.
(I've seen this before)

'the better?' is the wordplay.
I cannot quite understand how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found in the answer.
'better?' could be 'amend' (synonyms) and 'amend' is found in the answer.
The remaining letters 'men' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for amendment that I've seen before include "the fifth one benefiting Uncle Sam's defendants?" , "a bit of a change!" , "Addition or alteration, to a motion or official document, say" , "Corrective treatment" , "Change designed to improve a text" .)

I've seen this clue in The Globe and Mail.

'change for the better' is the definition. (I've seen this before) This is all the clue.

(Other definitions for amend that I've seen before include "Change, alter" , "Change for the better" , "Change to improve" , "Alter in writing" , "Make small improvements to" .)

I've seen this clue in The Mirror.

(Other definitions for upturn that I've seen before include "Improvement in business activity" , "Improvement, better trend in business" , "Recovery" , "economic improvement" , "Rise" .)

I've seen this clue in The Sun, The Irish Times and The Independent.

'change for the better' is the definition. (I've seen this before) This is the entire clue.

(Other definitions for improve that I've seen before include "Polish" , "reform" , "Get or make better" , "pick up" , "Become better" .)

(Other definitions for improvement that I've seen before include "Upgrade" , "Act of making better" , "Betterment" , "recovery" , "Enhancement" .)

I've seen this clue in The Times.

Change for the better? (9)