Put fellow off getting cleaner (9)

I believe the answer is:

detergent

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'getting cleaner' is the definition.
'detergent' can be an answer for 'cleaner' (chemical that cleans). I'm not certain of the 'getting' bit.

'put fellow' is the wordplay.
'put' becomes 'deter' (I can't explain this - if you can you should believe this answer much more).
'fellow' becomes 'gent' (synonyms).
'deter'+'gent'='DETERGENT'

'off' acts as a link.

Can you help me to learn more?

(Other definitions for detergent that I've seen before include "cleaner" , "Cleansing solvent" , "Soluble cleansing agent" , "Get tender (anag)" , "Synthetic cleaning substance for washing machines" .)

I've seen this clue in The Daily Express.

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