Tags I delete in BusyCal come back after a few minutes

Tags will continue to re-appear if they're being used by one or more events that are syncing in - deleting a tag sadly does not delete it from all existing events that use them.

You will have to remove the tag from all events that are tagged with this tag before it stops re-appearing altogether.

Also note: if you're using an Exchange account, you will have to delete these tags (that appear as Categories in Exchange) from your Exchange account using Outlook or Office 365 online portal

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