Delete old CSS

I’ve upgraded the theme to the latest responsive directory and am using a child theme that I generated in the child themes area. Now, I want to be able to change some of the styles such as the background color of featured listings.

However, any edits that I make to the child theme’s css file don’t affect the style. When I look at the source code for the page, I’m seeing the CSS in the page itself, repeatedly with dates.

Where can I clear this? and what is the best way to updated styles moving forward?

Thanks, in advance!