In order to offset the image on mobile resolutions and put some other part of the image in focus instead of center area which is displayed by default, please use the following approach:
Add Custom Id to desired section (mysection_1 for example):
And then add the following css statements to Appearance > Customize > General, Custom CSS field:
@media (max-width: 600px) { #mysection_1{ background-position-x: 400px !important; } }
This will offset image x position by 400 px only for device resolutions of up to 600px.
Adjust the numbers according to your needs.