I have replaced all files with core hacks with untouched originals and still receive this message:

Zenphoto has detected a change in your installation.

The script functions-basic.php has changed.

The change detected may not be critical but you should run setup at your earliest convenience.

What could that be?

Your change it is… Run setup so you get a new internal install signature.

Support build has also a way to ignore this if you know this is not an important change.

Oh. Once a change has been detected, it will be reported repeatedly until a setup is executed, even if the change has been canceled?

It also has to do with file times and some other stuff. Just re-run setup, it does no harm if all is already installed but will update the signature.