It's real easy to change the look of the Related Products display. Just create a sub-theme of your main theme and make your style overrides in the sub-theme.
If you have never done it a good way to learn is install the Zen theme and create a sub-theme using the STARTERKIT that comes with it. Then you add the CSS file and the avantlinker-block-item.tpl.php to your new sub-them.
The readme files in Zen and it's STARTERKIT will tell you how. It's very simple and will take you about 15 to 30 minutes.
Now you can make your edits in the sub-theme and leave your main theme untouched. It's not a good idea to edit core files of Drupal or in the themes and modules. That way when your site has updates available you don't have to worry about them over-writing your changes.
I loaded Zen up here today and with the sub-theme I created you can see a couple of test changes in the screen shot. Look at the xxx and the gray background for the price. Zen is good for learning, but you can create a sub-theme for any theme you are using.
AvantLinker: For this Avant post I turned "off" Related Products display.
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