Crossword Genius

Quickly remove kit covering a carpet (4,3,1,5)

Ross

I believe the answer is:

tear off a strip

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

'carpet' is the definition.
(I've seen this before)

'quickly remove kit covering a' is the wordplay.
I cannot really understand how this works, but
'quickly' could be 'fast' (synonyms) and 'fast' is present in the answer.
'a' is within the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for tear off a strip that I've seen before include "how to make it a bit narrower?" , "Reprimand" , "Carpet" .)

I've seen this clue in The Telegraph.
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