All of GJ has triggers, including integrations, so you could use CB Auto Actions to push an event to jEvents. Trigger as follows.

gjint_onAfterCreateEvent

Variables are as follows (needed to pass the event title, etc..).

$event, $group, $category, $user, $plugin

Example usage of the above variables in CB Auto Actions as follows.

var1_title
var1_event
var1_date

There is no documentation as incubator projects assume you're an advanced user. The below tutorial is for usergroup usage, but it shows an example setup of a trigger at the least.

www.joomlapolis.com/support/tutorials/107-use-cases/18237-assigning-usergroup-based-on-cb-field-value

You'll probably need to use a Query action and perform an INSERT database query to add the event to jEvents database. You'll use [var1_title] and [var1_event] substitutions for example to get the events information for the query.