Hair-splitter can raise fruit grower's hand (3-6)

I believe the answer is:

nit-picker

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'hair-splitter can raise fruit' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'grower's hand' is the wordplay.
'grower's' becomes 'nit' (I can't justify this - if you can you should give a lot more credence to this answer).
'hand' becomes 'picker' (picker is a kind of hand).
'nit'+'picker'='NIT-PICKER'

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

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