How can I delete a label from my Media Library?

If you'd like to delete an existing label from your Media library, so that it no longer shows as an option on your media, you'll just need to open up the "Filters" tab on the right-hand side of the Media library:
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Then click the "x" next to the label which you'd like to cancel:

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This will then remove the label from your list of labels, and also remove the label from any media currently labeled with it.