By default, Mailchimp Top Bar comes with responsive styling so that it shows nice on both big desktop screens and smaller mobile devices.

If you want to completely hide the bar on small screens then you can do this by adding the following snippet of CSS to your site.

@media( max-width: 600px ) {
    #mailchimp-top-bar { display: none !important; }

In this example, we are hiding the bar on all screens smaller than 600 pixels.

A simple way to add this CSS is by using the Simple Custom CSS plugin.