Most of the Divi options can be optimized for better user experience including options for small screens.

Landscape-oriented images may look great on Desktop but on small screens, they will be cropped because of the different aspect ratio. 

In this case, you can simply use a different image with a different aspect ratio, for example, 2:3 for a portrait image with the subject in the center. Generally, the height of your background image that you want to use for phones, should be at least 2 times bigger than the width.

You can define portrait-oriented images for Mobile and landscape-oriented images for Desktop.

I am starting my example with this landscape image:

And for the mobile background image, I've used this online tool to change the aspect ratio for phones:

All you need to check is Divi's Responsive options under the background image group where you want to define the afferent background image for each device:

Divi Builder Module Visibility Option

Different Layouts For Small Screens

Website Doesn't Look Good On Mobile

Optimizing Divi Layouts For Certain Mobile Devices