Crossword Genius

Tear sleeve of T-shirt off for rag (6)

Ross

I believe the answer is:

tatter

I'm a little stuck... Click here to teach me more about this clue!

'for rag' is the definition.
(synonyms)

'tear sleeve of t-shirt' is the wordplay.
I cannot really understand how this works, but
't' is within the answer.
'shirt' could be 't' (as in a T-shirt) and 't' is found within the answer.
an anagram of 'tear' is 'ater' which is within the left over letters.
No letters remain.
This explanation may well be incorrect...

'off' is the link.

Can you help me to learn more?

(Other definitions for tatter that I've seen before include "Torn shred" , "Become ragged" .)

I've seen this clue in The Times.
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