Black Bars in Email Signature

I am the graphic designer for a company. I know my way around Photoshop/Illustrator/inDesign... but have had issues when tasked with creating the company's email signature using Dreamweaver (I am not a coder).

Because I have no real knowledge of coding, I used an HTML signature template when asked to make our signature. But I sometimes get complaints from coworkers about issues with their signature. This is very stressful, as I really don't know Dreamweaver enough to troubleshoot or recognize issues and understand what's going on. I would greatly appreciate some insight from coders into what's going on and how to fix it.

In this case, someone has come to me complaining about black bars in their email signature that appear after exchanging a few emails. I've attached images of what the signature should look like, vs how theirs appears with the black bars (identifying information has been blurred out). 

Please let me know if you have any idea why these black bars appear and how to fix them!