Hello. Try this, see if it helps. If there’s not an option in the plugin settings, you should be able to go to your plugin code editor through your WordPress site backend (Plugins > Editor). Once there, select “Testimonials Widget” from the drop down menu of the upper right. You can then find the style.css file on the right panel. Once you have that loaded, just perform a keyword search (ctrl+F or Mac equivalent)for “background-color” or simply “color.” Once you find the background color line just change the color there. Take a look at this for more info: http://www.w3schools.com/cssref/pr_background-color.asp
Hope this helps!
Thanks for stepping in @jbmuzic.
@watp, alternately, check out the debugging CSS link on http://wordpress.org/plugins/testimonials-widget/faq/.