In theory you could parse their API response, and replace the image urls with ones pointing to an image proxy endpoint on your own server. That way the images would be retrieved by your server (let’s hope that’s not running on DigitalOcean as well ) instead of the info-beamer servers. Note that you might run into legal issues regarding API licencing in that case.
If the HTML page is the only thing you want to display on your screens, you might also use the Fullscreen Browser package instead. Then it’s the Pi itself that’s retrieving those images.