I am using this theme: http://www.eleventhemes.com/gridly/
In order for the pages to only show certain posts on certain pages it requires the category folder in front of the slug so if I have a page called graphic-design it has to be accessed this way: domain.com/category/graphic-design. When I go to edit the page in WP it automatically removes the / after the word category.
How can I add a folder name in front of the page name?
That sounds like a bug in the theme. My first guess is that there's a naming collision. I believe "category" is the slug Wordpress uses for displaying post categories, while the theme is trying to use "category" to rewrite page permalinks.
As an experiment, try editing Wordpress' built-in Category base option.
Try going to Dashboard > Settings > Permalinks, and at the bottom under "Category base" set the field to something besides "category", like "mycats" or whatever. For fun try setting it to "category" explicitly and see what happens.