Hey Chris ...
The "Reactions" element in your comments is a feature in the Disqus comment suite.
It's similar to a pingback, but was designed to showcase social media mentions of your content.
As you are seeing on your blog, someone used two of the available aggregation services "BackType" and "UberVU" to create a Twitter mention on the comment.
- "From twitter via BackType"
- "From twitter via UberVU"
To disable it, login to your Disqus admin panel (within Wordpress in Settings) then click on Settings and General. You should see a checkbox for Reactions - uncheck it and Save.
That's it ... those comments should disappear.