Well, no. They don't "give" you a quest. You actually have to go to a mission terminal and pick it up. This myth that it's handed to you in the mail or whatever is what drives the misinformation about why some players miss out getting this free tionese gear.
It is however the same mission terminal that gives you the daily and weeklies for HMFPs. Makes you wonder if they are missing out on those comms too.