HTML used in emails is a bit different than regular html, especially in a way how images are referenced. As images are in many cases attached to to the message, cid protocol is used to reference them:
<img src = 'cid:image1' />
What comes after "cid:" is the Content-ID of the referenced visual object.
This object must be attached to the email, and usually can be found in IMail.Visuals collection.
You have several options:
Save all visuals elements to disk (or memory or database), parse and rewrite HTML, so each time cid: resource is referenced you reference your server:
cid:image1 -> https://example.com/visualsprovider?id=image1
Inline all images so base64 is used:
<img src='data:image/jpeg;base64, LzlqLzRBQ...BASE64DATA' />
You can use IMail.SaveHtmlAs or IMail.GetBodyAsHtml methods with inlineVisuals parameter set to true for that purpose.
Hope this helps.