Rick You delete a tuning style by swiping horizotally and then choosing "Delete", but I guess you have already discovered this.
A tuning document in which you used the custom style still contains a copy of it, because a tuning document you send to a different device needs to work there, too. The custom tuning style will automatically be re-added to your list of custom styles if you open a tuning document which still contains it. So currently, to permanently get rid of it, you have to manually open each tuning document and select a different style, and then delete the custom style.
As I know that you have tons of tuning documents, this would be a tedious process.
In a future version, I could improve this by not automatically recreating the style from the document but rather only offer it as an option in an alert.