We have already removed the exit application (your method works, but I also used the method where I deleted the application from the boot disk). If I do this and press the red marked button (see image), the tinycore GUI shuts down and tinycore starts in command line mode. And I'm trying to prevent this situation from happening.
But I guess I got the idea. The menu that opens when you click on the screen is part of the FLWM application, if I modified the application so that it did not contain the menu, the problem would be solved.
And you might be wondering why I am trying to remove command line and terminal from linux. The explanation is simple, I am making a tinycore distribution that is supposed to be an alternative to Chrome OS. You can visit my website and download the OS.
http://gogleos.xf.cz/The website doesn't look very good (I made it quickly in MS word).