Hey GabiClayton 🙂 Let me see if I understood, what you want is to get rid of the grey line beneath the menu when the page is long to scroll down?
If so, you have two choice, going to Appearence > Editor and changing one line of code in the style.css file. If you’re afraid you might change something you don’t want, you just can install the Simple Custom CSS plugin: http://wordpress.org/plugins/simple-custom-css/
You can try reduce height of browser window and try to understand why it happens with sticky header. With your small content and big header only way it’s disable sticky header in theme options > header.
Meiji, your css code can be easy insert to the custom css in theme options without plugin installation.