You can suppress the ugly pop-up window – but keep the less obtrusive Gnome Shell notification – by setting /org/gnome/evolution-data-server/calendar/notify-with-tray in dconf.
I discovered this from a comment in a related evolution-data-server bug report (GNOME/evolution-data-server#60).
Option 1: Use dconf Editor
Install dconf Editor if it's not already installed:
sudo apt install dconf-editor
Launch dconf Editor:
Navigate to /org/gnome/evolution-data-server/calendar and set notify-with-tray to "on":
Option 2: Use
Alternatively, a quicker way to turn this setting on is to issue following command in the terminal:
gsettings set org.gnome.evolution-data-server.calendar notify-with-tray true