How can I remove sync from a cloned ecommerce store?

I’m not really sure the technical details of how they are doing this. I don’t think there are any malware files added to your site, it all happens on their servers. I think they are pointing their own domain name at your website and when a request is made to thier-aliased-domain.com, your site content is run through some sort of find and replace script on their server with your content. It’s not a copy of your site, it is your site but served to the browser after being modified.