The mod to the M3 hires card effectively excludes the 8Ch-8Fh ports. Normally the M3 hires card lazy address decodes so that the CRTC registers (ports 88h and 89h) are quad addressed (mirrored) in the 88h-8Fh range. This isn't a problem with the M3 because it doesn't use ports 8Ah-8Fh for anything.
However the M4 tech ref manual lists ports 8Ch-8Fh as "Graphics Sel. 2", and these are sometimes called the "undocumented" M4 hires ports (actually documented on p189 of https://archive.org/details/TRS80Model4PServiceManual and summarised at http://www.tim-mann.org/trs80/ports.doc.txt). So if M4 software tried to use these ports with an unmodified M3 hires card, then potentially the CRTC registers would be sent rubbish data causing all kinds of problems. The mod to the M3 hires card prevents this from happening.
I'm not really sure what the mod to the M4 mainboard is doing, however it's effectively stopping the DOT* signal (which appears to be a sync signal) from being used. The relevant part (U22 pin 12) is shown in the schematic on p35 of the M4 tech ref manual (26-2110). As a hunch perhaps it's disabling the sync from the M4 mainboard because presumably the M3 hires card has its own sync? Maybe someone who knows more about video electronics can explain.