I can see how to add a badge (is this the correct term for what’s in this screenshot?)…
… to a note in both map and outline view. I cannot find at atbref how to delete the badge from the note
In the upper left-hand corner of the badge picker, you’ll see an empty space. That’s “no badge”.
Ahhh 
Thank you.
In the article on Badges it links to the more detailed article on the Badge pop-up picker and states:
Clicking the first (blank) tile in any set resets the Badge to the default inherited state.
Which is to have no badge—if unsure see here.
Given the range of tool/feature combinations in Tinderbox it is impractical to write a short complete answer for any possible question. The links are there with the assumption that people will follow links and look up and learn what they don’t know. Plus. individuals’ terminology differs so one can’t always assume that a search for one’s personal choice of term will work on just one question. In the 18 years the badge feature has been documented (it was added in v4.0.0, see) there has never been a problem before with the descriptions offered.