Hi there, 

I'm clearly doing something wrong. I've setup custom badges for groups and they are displaying just fine in my profile cards. 

Question is ... How do I remove the text label above them? See image ... 

It would require customisation to the templates to achieve this. Probably Forums->Front->Index->Post

Is there a better way to achieve what I'm trying to do here? 

1 hour ago, EvanDC said:

Is there a better way to achieve what I'm trying to do here? 

I'm afraid, there is not something in the core software which does this. The primary group name would show in addition to the group icon.

Assuming it matches up to the default theme - can't verify this will work for you as no idea what your site code looks like...

.cAuthorPane_info > li[data-role="group"]{
  display:none;
}