It is stored in config file as
<option id="rss.rss.checkUpdates" value="true"/>
Replace the value with
false to switch it off.
Config file sits in user's home folder and is named
.ganttproject so you can just take the default file (generated after the first start) and replace it with modified one.
We recommend to keep it on, though. Traffic is very low, it won't break if you have no internet and there is no spam (you can find all previously published news here: https://ganttproject-frontpage.blogspot.com/
If you switch it off, we recommend subscribing to any of the news channels to stay tuned.