Part of a nasty eyelid (4)

I believe the answer is:

stye

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'part of a nasty eyelid' is the definition.
'stye' can be an answer for 'eyelid' (I have seen 'Inflamed eyelid ' mean 'stye' so perhaps 'eyelid' could also mean 'stye'). I'm not certain of the 'part of a nasty' bit.

'of a nasty eyelid' is the wordplay.
'of' indicates the answer is hidden within the clue.
'STYE' is hidden in the letters of 'nasty eyelid'.

Can you help me to learn more?

(Other definitions for stye that I've seen before include "dump" , "Infection on the edge of the eye" , "Swelling near the eye" , "Ocular inflammation" , "irritation to the viewer" .)

I've seen this clue in The Globe and Mail.

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