A cat’s lost by flap (3)

I believe the answer is:

tab

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'flap' is the definition.
(both can mean a small piece of material)

I don't understand how the rest of the clue works.

(Other definitions for tab that I've seen before include "Small flap - bill" , "The bill in a restaurant" , "Ring pull" , "Tag" , "Flap; meal bill" .)

I've seen this clue in The Times.

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