Without getting into the relative merits of open versus injectable fat grafting, here's a definition.
By "open" it is meant that an incision is made. This is in contrast to injectable technique, where a needle is used to introduce the graft.
Transconjuctival means that the tissue is introduced through the conjunctiva, which is the inside layer of the eyelid, that which is in contact with the globe of the eye.
Composite tissue has two or more types of tissue layers. Examples are dermis-fat grafts, cartilage-skin grafts, etc. In this case, the graft is usually dermis-fat.
Fat can be inserted as micro droplets, as is succesfully done by many, or as a layer of tissue. Whether fat remains alive or not depends on the fat tissue getting a source of blood supply in a timely manner.
Dr. Seckel's otherwise informative answer is no completely accurate in the fourth sentence where he states "Fat injection techniques kill a great many of the injected fat cells so that survival of the fat is very difficult to predict. In addition lumps and irregularities are common following fat injections in the eyelid area-the eyelid skin is so thin that any irregularity beneath the skin is very visible."
This is indeed true in inexperienced hands, however I, and many others who follow techniques well described and codified by Sidney Coleman, have years of excellent track record.
Conversely, many others who have attempted Dr. Seckel's technique have not had as reliable and expert results as he has.