Writer let tiny letters out with contrition (10)

I believe the answer is:

penitently

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'contrition' is the definition.
(thesaurus)

'writer let tiny letters' is the wordplay.
'writer' becomes 'pen' (something which writes).
'letters' indicates an anagram.
'let'+'tiny'='lettiny'
'lettiny' is an anagram of 'itently'.
'pen'+'itently'='PENITENTLY'

'out with' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Daily Express.

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