Are the background images replaced?
ShortPixel Adaptive Images (SPAI) by default can replace the URLs of the images used as background only if they are included inline in the HTML of your website.
If the images are included in external CSS files, then SPAI won't be able to find and replace them unless you enable the Replace in CSS files option. To do this, go to Settings > ShortPixel AI > Advanced and enable Replace in CSS files, as you see in this image:
If the background images included in external CSS files are served from a different domain than yours, you should include such external domain in the Additional CSS domains box. Example: