GB Pro which we aim to release later this month will have responsive background controls.
In the free version if you want to display a different background image for mobile then you could do this:
1. Select the Container Block and in settings > Advanced –> Additional CSS Class(es) – give the element a class eg. mobile-background
2. Add this CSS using your CSS class:
.gb-container.mobile-background {
background-image: url(full_url_to_your_mobile_iamge);
}