You will need the Write Notes permission to perform this action. It is campus-scoped, so a campus override can change it at one campus. Deleting a note on one person needs the permission at one of their campuses, but deleting a family note needs access at every member of that family. See People for what the permission covers, and Campuses and organizations in Version 8 for how campus access works.
Delete a note
Navigate to the person's profile and click the Notes tab.
Locate the note you want to remove. Click the 3-dots menu at the beginning of the row and choose Delete.
In the confirmation pop-up, type in the confirmation message and click Confirm Delete to finish.
Tip: Notes of type Archived Notes and Unarchived Notes cannot be deleted.
Tip: If Delete is refused on a family note, a member of that family is at a campus you cannot reach. Someone with wider access can remove it, or you can edit the note so it applies to this person alone.