Mistake made teen change for the better (8)

I believe the answer is:

emendate

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'change for the better' is the definition.
Both the definition and answer are verbs in their base form.
Maybe you can see a link between them that I don't see?

'mistake made teen' is the wordplay.
'mistake' indicates anagramming the letters.
'made'+'teen'='madeteen'
'madeteen' anagrammed gives 'EMENDATE'.

Can you help me to learn more?

(Other definitions for emendate that I've seen before include "Fix" , "Correct" .)

I've seen this clue in The Times.

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