Using Mozilla inspector I find that it is the following template code that is causing it:
.art-textblock ul > li::before {
content: url("../images/postbullets.png"

The button is in a structure so the ::before is causing the dot - which is actually a list item bullet point graphic to appear.
I don't want to just remove it from the template (which is generated by Artisteer) as I assume it will affect the appearance of bullet lists in my site content.
...if this is an Artisteer issue do say and I'll go ask them - I don't expect you to help unless it is an issue with EP !