Noting you could re-programme the PIC or use it for a project and then return it to the display once re-programmed with the original code. I've re-programmed mine with my own start-up message.
Not on the AXE033!
Source code is only provided for the PICAXE-based AXE133.
The AXE033 uses a raw PIC so there would be no way to restore its original functionality if you reprogram it in a PIC programmer as no source is provided. If the AXE033 has code protection (like the PICAXEs themselves do), then reprogramming it with whatever the programmer read out of it will also result in a non-working AXE033.
I'm not aware of the existence of an official schematic, but for making one the
pinout of the pre-programmed PIC itself is a good place to start. Again, this pinout was
not provided by Rev-Ed.