File URL of media that has been uploaded befor mapping domain


I've just realized (when using the plugin smush it) that when I setup an website on multisite ( and build the whole website there and also include pictures etc. the file URL of pictures und media stays the same after I map this website to the real domain (
I'd like to run "smush it" to reduce image size but that only works if the mediafiles are from the new domain. Also I could imagine that concerning SEO that is not perfect, if the images are included from the main domain - I guess?!

So to my question - do you know a way, I can (automatically - if possible) change the file URLs to the new domain?

Thanks in advance & greetings!