Hey there! I'm going to have to look into the Embed BG option, as I've never done an embedded html game before.
I couldn't find anything in the itch documentation on Embed BG...just this comment in the forums: https://itch.io/t/213380/whats-embed-bg-in-the-theme-editor
From some initial poking around, it looks like the image is being assigned to this div with the game_frame class on it. It appears on both the iframe and click to fullscreen embeded game variations.