Target Post Categories

Greetings community,

I have looked all over the internet but cannot find an answer to my question. It seems like it should be easy - but it hasn't appeared to be so far.

Does anyone out there know how to target specific post category links to style them? I want to add a simple background to each category link but am having no luck.

Here is the link to the page and I will attach a screenshot so you can see what I am trying to achieve.

Thanks everyone!