Just a quick troubleshooting article on this one, as it can be a nuisance but it is very easily resolved.
You may find that when you go to Modify, or Delete a custom slicer style you’ve created that nothing is happening. It will still let you Duplicate, but that just leaves you with a load of redundant custom styles sat in your Options.
The simple solution is you have a worksheet protected somewhere which you need to unprotect. It won’t be the worksheet you’re already in, but another on the workbook. Temporarily unprotect it while you Modify/Delete your custom styles and then re-protect afterwards.