FYI...
If more than a single instance of a gadget is open, either in the same dashboard or a different one, it can't be deleted.
When you edit the gadget and click on the Delete button the gadget disappears giving the impression it has successfully been deleted but if you refresh your screen (F5) it reappears.
If you close all instances of the gadget except the one you will edit, it will delete.
I opened a case which resulted in a defect being created and referred to Engineering.
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Kevin Boyle, SuperUser
Calgary, Alberta, Canada