Crossword Genius

Viral treatment recalled irritation with hesitation – privy to containing that (10)

Ross

I believe the answer is:

interferon

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'viral treatment recalled irritation' is the definition.
I can't tell whether this defines the answer.

'with hesitation privy to containing that' is the wordplay.
'with' means one lot of letters goes inside another.
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'privy to' becomes 'in on' (I've seen this before).
'containing' means one lot of letters goes inside another.
'that' becomes 'terf' (I can't justify this - if you can you should give a lot more credence to this answer).
'er' placed inside 'inon' is 'ineron'.
'ineron' enclosing 'terf' is 'INTERFERON'.

Can you help me to learn more?

(Another definition for interferon that I've seen is " Protein inhibiting virus replication".)

I've seen this clue in The Guardian.
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