The Idgon plugin will only transmit data when the extension button is clicked. The only information sent is the hostname of the currrent tab which is used to lookup any Idgon's associated with that hostname.
the code to isolate the hostname is very simple and is considered safe:
var current_url = current_tab.url;
var url = new URL(current_url);
host = url.hostname;
This code should not transmit any sensitive URL parameters or request paths.