Just replying to myself again.
I took the time to read up on how filters work in the code that allows you to hook in and change what the plugin outputs.
For anyone wanting to change the markup that the plugin returns please take a look at this article. It explains the concept of filters and how they work in Wordpress. This will allow you to place a function in your child theme’s functions.php file to modify or completely swap out any content that is being passed through a filter, something which the wp-discourse plugin takes full advantage of.
You can see an example of that in the wp-discourse code on github.