It's possible to delete customized or cloned Portal elements. Default Portal elements (those created and established by Finalsite during site deployment) can't be deleted.
You can tell whether an element is custom or a default by hovering over them in the library. Custom elements will display icons allowing you to edit or delete the element template, as well as any elements that were created with it.
The default elements will not have any "Edit" or "Delete" icons appear when you hover over them.
When you delete an element, you can choose to delete only the element template from the Portal element library, OR to delete ALL of the elements made FROM that template on the current portal page. (The default is to only delete the template, and not to remove any existing Portal elements.)