I'm surprised about this too, and it seems that plenty of people on the internet have asked about this as well. The only solution I could find is basically a hack, although simple enough:
sudo mv /usr/share/sounds/freedesktop/stereo/camera-shutter.oga /usr/share/sounds/freedesktop/stereo/camera-shutter.oga.bak
This renames the audio file that gets played when taking a screenshot. I suspect it will be restored after certain updates, however. A setting for this would be a nice addition to GNOME, but maybe Zorin OS could implement it separately as well.