This would delete the relationship (i.e. "the link to attachment", as you've mentioned), not the attachment itself. If the goal is to delete the attachment as well (so that it doesn't take up space, for example), then most likely SO_ATTACHMENT_DELETE would help. For OBJECT_ID I'd guess you'd have to read the attachments first.
Anyways, if this has been resolved, kindly close the discussion.
Thank you.