Please keep in mind that even if this automated check is disabled, users can just open Edit > Settings > App updates and bypass these options. There is no 100% working way to prevent users from installing the update (well, unless you make the update directory, $HOME/.ganttproject.d/updates, read-only)
However, if you’re happy if users just can’t install updates from the user interface, you may change the value of the update URL and point it to your own update resource. It shall be accessible over http(s) and is supposed to be a JSON. A simple text file with the following JSON inside: [] (empty array) is okay.