What's left after smoothing affairs across Italy? (7)

I believe the answer is:

filings

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'what's left after smoothing' is the definition.
I can't tell whether this defines the answer.

'affairs across italy?' is the wordplay.
'affairs' becomes 'flings'.
'across' means one lot of letters goes inside another.
'italy?' becomes 'i'.
'flings' placed around 'i' is 'FILINGS'.

Can you help me to learn more?

(Another definition for filings that I've seen is " Iron particles".)

I've seen this clue in The Telegraph.

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