Crossword Genius

NY hotels refurbished in an inconspicuous manner (2,3,3)

Ross

I believe the answer is:

on the sly

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'in an inconspicuous manner' is the definition.
I can't tell whether this defines the answer.

'ny hotels refurbished' is the wordplay.
'refurbished' indicates anagramming the letters.
'ny'+'hotels'='nyhotels'
'nyhotels' with letters rearranged gives 'ON THE SLY'.

Can you help me to learn more?

(Other definitions for on the sly that I've seen before include "under cover" , "Secretly or furtively" , "With craft" , "Behind someone's back" , "Surreptitiously" .)

I've seen this clue in The Times.
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