How to stop embedded signature images from showing as links in Apple Mail?

As a business, we use Exclaimer signatures which attach a signature server-side to all our emails. We send these out, and it's all good and well.

The signatures appear properly on Outlook for Windows, macOS, iOS, and Android, but does not display correctly inside Apple Mail. Despite using embedded images, they still display as URLs.

How do we get our signature images to load correctly for external recipients who may use Apple Mail as their default mail app on iOS and macOS?

[Re-Titled by Moderator]

Original Title: How do we stop signature images showing as links instead of actual images, despite using embedded images?