Post History

This isn't a direct answer to your question, but a suggestion.  Try specifically disallowing internet access to this program in your firewall.  That may cause the program to realize it can't get to the internet at all and to stop trying.

It is unlikely that the writers of the software always required an internet connection for the software to work.  They apparently didn't deal very well with the case of internet access but no access to their servers.  Perhaps by denying internet access completely, the software will let you continue.  You may then be able to disable the call-home "feature".  If not, you'll have to put up with some broken internet access message each time you start it.

<hr>

I just noticed your answer where you unplugged the network cable.  Badly written software like that is annoying, especially if you can't disable it calling home.

Using the firewall to effectively make your internet look unplugged to only that program might be a useable way to proceed.  You may still have to dismiss the popup every time you start the program.

You could also look around for where this program keeps static settings, like whether to check for updates or not.  In Windows, that would be in the registry.  MacOS probably has something equivalent that others here would know more about.  Sometimes poking around in the registry to see what settings a particular program has can be quite useful.