If the Business Object is set to No deletion you will not be able to delete an entry within this business object.
That's also the normal behavior for Collection objects.
Thanks for the reply. I was afraid of that. I find that odd that adding an attachment would be a "one-way" process - what if I inadvertently add one and want to delete it. I suppose I could go through the process of recreating the Attachment business object, but that seems like too much work at this time.