The complaints were made following the family's removal from a hearing last year.
GSOC has been granted access to a court's backup audio recording system as part of its investigation into allegations made by members of Enoch Burke's family.
The complaints were made to the Garda watchdog after Enoch, his parents, brothers Isaac and Simeon, and sister Ammi, were removed from a hearing last year.
Enoch Burke challenged GSOC's request, claiming the use of the backup system amounted to "covert surveillance" that breached his right to privacy.
However, the Court of Appeal rejected all of his arguments today before deciding that GSOC had established legitimate reasons for handing it over.
They will now be able to listen to the ambient recording from the moment the judges rose that day to when the courtroom was cleared.