The creator of a saved search can delete that search at any time.
If that saved search was shared across the organization, an Owner can delete that shared search only after it has first been deleted by the creator in order to prevent shared searches from being deleted by anyone other than the creator of that saved search.
A shared filter will also honor any restricted categories, similar to how a normal filter and search would.
Instructions
Navigate to the Requests tab
Open the Saved Searches dropdown
Click Delete next to the search you wish to remove
Select Confirm on the pop-up that says Are you sure you want to remove this saved search?