It looks like a thin bungee cord going from the girth, through the bit, then through several keepers on the cavesson, including the tab for the flash. It is designed to put pressure on the nasal bone if the horse tries to lift his head (apparently the rider is incapable of getting/keeping the horse - ahem - flexed in the neck without mechanical help). The device looks abusive to me - since it is fixed to the girth, there is no release from it.
Scuttlebutt is that it was either a left over piece of equipment from the Arabian world, or it was devised by the rider’s very well known European trainer (who frequents Welly World during the show season).
[Edited text and image to discourage speculation about the rider’s identity.]