Personal matter of dubious value is not raised online (6)

I believe the answer is:

tonsil

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(Other definitions for tonsil that I've seen before include "No slit at the base of the tongue" , "One of two at the back of the mouth" , "Mass of tissue" , "One often removed" , "Lymphatic tissue at the back of the mouth" .)

I've seen this clue in The Guardian.

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