Transconjunctival Blepharoplasty and Fat Grafting for Hollow Eye Area?

This solution may not be as silly as it sounds on first blush.
The bulge of fat is due to a bulge in the infraorbital fat behind the orbital septum. Transconjunctival blepharoplasty removes the fat, causing it to bulge less.
The hollowness most patients complain of is lower than the infraorbital fat bulge. There are two basic solutions to this problem:
1. Take the existing fat and redistribute it. This requires dividing the orbital septum at the arcus marginalis, a maneuver that can predispose to pulling down of the lower eyelid. This can be done through an incision in the lower eyelid and also through a transconjunctival incision.
2. Take the fat out of the transconjunctival sac and then put in separately a graft into the hollow area below the eye
Of the two, I have come full circle and no longer do fat repositioning. The grafts tend to clump and retract to where they had been previously. Often, the lower eyelid bulge returns. I think this is due to the fat still being attached to the lower eyelid fat pocket. If the fat is detached in order to avoid this problem, it becomes no different than a separately placed graft. Plus the arcus marginalis layer has been violated, predisposing in my opinion to the potential of scar formation. The most quoted series in the literature is only 24 patients, far too low to be confident of the safety of dividing the arcus marginalis method, in my opinion. I have seen plenty of unhappy repositioning patients where they did get alteration in eye shape (usually drooping, usually subtle but nonetheless there).
So we are back to square one, as they say.
I prefer to reduce transconjunctival fat and then place separate grafts, but not fat injection, where the grafts are largely traumatized, but untraumatized fat fascial grafts (LiveFill (R), almost always in combination with an ultrashort incision cheeklift (USIC). This elevates cheek volume.
Even with these 3 measures, patients must expect conservative results. That's how tricky the under eye area is if you don't want to subject the patient to great risk of lower eyelid eye shape change.
Just my opinion.

Dear Pepys
It is impossible to know your issue without a personal consultation.
However, in general it is always much safer for you to have lower eyelid surgery from behind the lower eyelid transconjunctivally. Then the fat is removed from the lower eyelid using a skin incision, the surgery uniformly damages the nerves that supply the lower eyelid muscle responsible for holding the lower eyelid firmly against the eye. Additionally the scar tissues that develop following this surgery plus any skin the doctor is tempted to remove risk causing the lower eyelid to be pulled during the healing process.
Transconjunctival surgery developed about twenty-five years ago was the answer. Except that we noticed that despite this better approach, as patients healed (an this was also true for transcutaneous lower eyelid surgery) the lower eyelid looked hollow because the fat was hiding the tear trough groove at the top of the cheek. To address this issue, it is now common at the time of tranconjunctival lower eyelid surgery to rotate a living pedicle of lower eyelid fat into the tear trough hollow. This procedure is called an arcus marginalis release. It is possible that this is what your surgeon was describing.
Performing lower eyelid surgery and then grafting free fat form a second site to compensate for the volume removed does not make a whole lot of sense.