Carter had won the 4x100 metres relay gold in the Chinese capital along with Michael Frater, Asafa Powell and global superstar Usain Bolt in a then world record time of 37.10sec.
But it emerged in June that retests of frozen samples had allegedly uncovered traces of banned stimulant methylhexanamine in both A and B samples.
If his failure is confirmed, Jamaica could be stripped of their gold medal.
A hearing was held in Lausanne last week in order for evidence to be presented to the three-strong IOC panel consisting of Swiss chair Denis Oswald, alongside Turkey's IOC vice-president Uğur Erdener and Swedish Executive Board member, Gunilla Lindberg.
According to the Jamaican Gleaner, Carter was represented by Kate Gallafint of London-based legal firm Blackstone Chambers.
He enjoyed additional support from Kendrah Potts of the law firm Mishon de Reya, which has offices in London and New York.
Legal officer Jean-Pierre Morand and medical and scientific director Richard Budgett reportedly represented the IOC.
Jamaican Olympic Association President Mike Fennell was also present, while Carter participated via video link.
Carter also earned a gold medal in the 4×100m relay, alongside Bolt, at London 2012.
He was also a member of the 4x100m team which won gold medals at the 2011, 2013 and 2015 International Association of Athletics Federations (IAAF) World Championships in Daegu, Moscow and Beijing respectively.
Carter also a won a bronze medal in the men's 100m at the 2013 World Championships.
IAAF anti-doping rules appear to suggest that any athlete retrospectively caught doping will be stripped of all subsequent results up to the present day, although others believe a ban of just two year is more likely.
It is not yet clear exactly when a verdict will be announced.
The IOC are gradually holding hearings and confirming cases into all the athletes who failed Beijing 2008 and London 2012 retests.
Russian weightlifter Apti Aukhadov was the latest to be stripped of a London 2012 silver medal last week after failing for anabolic steroids turinabol and drostanolone.
The Carter case is additionally complicated because methylhexaneamine was only added by name to the World Anti-Doping Agency (WADA) banned list in 2010, although it was indirectly banned before then.
"Methylhexaneamine is a stimulant developed in the 1940s and according to the Prohibited List, all stimulants are prohibited in competition (Section S6)," a WADA spokesman told insidethegames.
"It was always a prohibited substance, under a catch all category, but was added by name from 2010 onwards."
Carter could therefore also face a backdated ban of two-years, the maximum sanction for the offence at the time of the WADA rules, although some past methylhexaneamine cases have resulted in a warning rather than a ban.