The app specific right click contextual menu is defined in the .desktop launcher file of the application, which is effectively in use. On a system, multiple launchers with the same name may exist. Only one will be used. Only changes in that specific .desktop file will have effect.
.desktop launchers on your system matching the label you see in the Application Overviews or in your menu system (other Ubuntu flavours) can be found with a find command:
find / -name '*.desktop' -exec grep -H "Name=<what you see in the menu>" {} \; 2>/dev/null
Only .desktop launchers existing in an applications directory can be in effect. If you find multiple results, you already can discard those for which the directory path does not end with applications.
Then, for the remaining ones, a .desktop file residing under your home folder in ~/.local/share/applications will take precedence. Otherwise, precedence is determined by the order in which the parent directories of applications are listed in the variable XDG_DATA_DIRS
$ printenv XDG_DATA_DIRS
/usr/share/gnome:/usr/local/share/:/usr/share/:/var/lib/snapd/desktop
Thus, a .desktop file living in /usr/share/gnome/applications will take precedence over a file with the same name in /usr/local/share/applications, etc.