It would make a lot of sense to be able to just remove style ITEMS that you don't need/want right when you are most likely to see them - in the style ITEM picker. Right-clicking does nothing; in the case of the gallery view within the symbology pane, it actually acts as a left click. To actually remove the style ITEMS, it's a pretty cumbersome, unintuitive trip through the catalog view:
- insert
- catalog view
- styles
- favorites
- manage
- show
- style class
- right click & delete.
Would be a lot simpler to just remove them from here.

(Would also helped if the style categories functioned like folders in catalog view).