How can I delete a tag from my Media Library?

If you'd like to delete an existing tag from your Media library, so that it no longer shows as an option on your media, you'll just need to open up any media containing the tag within the Media Library. 
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You then need to click the tag you want to delete, and then click 'Delete Tag'.

​This will then remove the tag from your list of tags, and also remove the tag from any media currently labeled with it.