PHP knows the domain from the server-call. If your site is on a specific server, you might have several urls pointing to this server. Your PHP does not know by itself which domain he has. Only from the request that the user is doing PHP is getting this information in the $_SERVER-var that Typo3/Extbase can read. I assume your script is running on different servers if you want to get the url? Can you put a configuration on the server that is different for each server?
One approach to do this would be to store the url from a user-call and read this in your Background-Module.