CSS is what styles the theme. Colors are added via CSS. So access to the CSS files is important. If you get access to the CSS files then yes you should be able to colour the quiz feedback section.
Here are some CSS selector ids and classes which make up the sort of thing you may need. I have just added block colours to show where the colour code goes. The first 2 are the headers so the color white in this case colours the text only. Whereas the last three are background specific.
If you do manage to get access to the core.css for the binarius theme, then open it using Notepad, copy and paste these into it. Save it and load it back to the server, to overwrite the one on the server.
That done You will need to clear Moodle cache by going to Site Administration > Development > Purge all caches. That done...test to see if you get any bold red/green or blue backgrounds in the quiz feedback areas. If you do well all you need to do then is find the colour code for the color you want to use in the CSS. Like #D0F3D6 which is the color of the background it's in.
#page-mod-quiz-view .generalbox#feedback h2 { color: white;}
#page-mod-quiz-view .generalbox#feedback h3 { color: white;}
#page-mod-quiz-view #page .quizgradefeedback { background-color: red;}
#page-mod-quiz-view .generalbox#feedback { background-color: green;}
#page-mod-quiz-view .generalbox#feedback .overriddennotice { background-color: blue;}
HTH
Mary