Strangely proper, sweet kids may exert such an influence (6,5)

I believe the answer is:

pester power

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'kids may exert such an influence' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'strangely proper sweet' is the wordplay.
'strangely' is an anagram indicator.
'proper'+'sweet'='propersweet'
'propersweet' with letters rearranged gives 'PESTER POWER'.

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I've seen this clue in The Times.

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