I know how to embed an image, but the receiver still sees an attachment icon and they are looking for an attachment.
Does anyone know how to keep that icon from appearing on the receiving end?
It depends on the Mail client of your receiver. If it does not support Rich Text and HTML, in the sense, does not offer a complete/true email experience, then images are shown as attachments. Most smartphones sometimes do show images as attachments.
AFAIK, you don't have anything to do with this (or can do anything about it).