ETA: If you are on the newer Squarespace 7.1, this post has a walkthrough: How to Show a Different Banner Image on Mobile in Squarespace
Hi @Joeyearthly,
If you are using an index page, I have a different workaround that I like a bit better, since you can make whole area specific for mobile instead of just the banner image. I create two "sub-pages" at the top of the index page, one for desktop view (with the URL slug home-banner) and one for mobile view (with the URL slug home-banner-mobile). Then I add the following code to Custom CSS. (Note that if you want to edit the mobile from your desktop, you'll need to briefly comment out the code so you can see that page on desktop.)
/* show home page block dependent on screen size */
@media only screen and (max-width: 780px) { #home-banner { display: none; } }
@media only screen and (min-width: 781px) { #home-banner-mobile { display: none; } }