Crossword Genius

Starter taken off mat that's greasy (4)

Ross

I believe the answer is:

oily

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'that's greasy' is the definition.
(synonyms)

I cannot understand how the rest of the clue works.

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(Other definitions for oily that I've seen before include "Like a lot of fish" , "Oleaginous" , "Unctuous" , "Smarmy" , "Viscous" .)

I've seen this clue in The Times.
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