While all of the Gree Event quests are picked up from the Mission Terminal at your faction base, there is one hidden quest that you can find aboard the Grey Secant (make sure you have purchased access to the Secant from the Event Vendor – requires Newcomer Reputation or greater with the Gree).
You only have access to starting and completing the Quest during a Gree Event so don’t let time run out!

As you board the Grey Secant, head north following the map, and just before the drop-ledge zone if you look carefully there should be a Friendly Gree Droid named Kanarosiku-K offering you a special quest!
Talking with the Gree Droid, they will ask you to find it’s Gree Droid friends that have been scattered and hidden across the galaxy, and in return will offer you a stack of event currency and a Gree Mini-Pet L1-L.

You must talk with all of the droids that are hidden across Alderaan, Tatooine, Quesh, Hoth and Voss. Additionally there is one more set of droids on Coruscant & Dromund Kaas however you only need to go to your own factions homeworld to complete the quest.
Don’t be too worried about locating them, they will appear on the planetary map as quest markers, alternatively you can watch this great production video by Corellian Run Radio if you still require additional help:

Once you locate all of the droids hidden across the galaxy, return to Kanarosiku-K on the Grey Secant before the event ends and you’ll be reward your own Gree droid Mini-pet.