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.