Hi Ryan,
Take a look at the screen shot. You can see I added the line:
list-style: none outside none;
And the bullets disappeared. If you want to edit layout.css you can add this line at the bottom. But when you update your template your changes will be overwritten.
The best thing to do is make a child theme for this site. Then add new rules to the layout.css file you create in the child theme. These will overwrite the original style sheet.Then when there is an update your changes won't be wiped out.
Create new rule for li in the child theme. to redefine how it works.
Also this site is using cache very heavily, which is good, but you may not see your changes until you clear the cache completely and maybe even refresh your browser.
See if that helps.
Cheers,
Ed