The dispute centres on whether the eight-year sentence a U.S. military commission handed him for war crimes should be interpreted as a youth or adult sentence.
However, the arcane technical legal battle has taken on loud political overtones.
"This case is another illustration of the heavy-handed approach Canada has consistently taken towards him," said Gillian Hnatiw, who represents the Canadian Civil Liberties Association, which is intervening in the case.
Khadr, 28, was released on bail last week after almost 13 years in custody while he appeals his U.S. conviction, which has drawn fierce criticism from legal and human rights experts.
Although he was 15 when his crimes occurred in Afghanistan in July 2002, the military commission made no distinction between juveniles and adults in sentencing him in 2010 to a further eight years behind bars.
The federal government, which has consistently branded him a hardened terrorist and is separately fighting his bail, argues Khadr was really given five concurrent eight-year terms for each of the five war crimes to which he pleaded guilty.
While the government concedes the sentence for the most serious charge — the murder of an American special forces soldier — can only be considered a youth sentence, it argues the other four — including attempted murder — must be viewed as adult sentences.
No provisions exist for an inmate to serve both youth and adult sentences at the same time, so Ottawa classified him as an adult offender when he transferred to Canada from Guantanamo Bay in September 2012 under an international treaty to serve out his punishment.
Khadr's lawyers — with the unanimous backing last July of the Alberta Court of Appeal — argue he is serving a single global sentence of eight years, which can only be interpreted as a youth sentence.
They argue the Harper government is simply being vindictive as it pursues a political tough-on-terror-and-crime agenda.
Because Khadr is no longer in custody, the outcome of the Supreme Court case may end up having little direct impact on him, and his situation appears to be unique and unlikely to be repeated.
"It's difficult to see how this could affect anyone else," Nate Whitling, one of Khadr's lawyers who will argue the case, said on Wednesday.
"But it's got the (Khadr) name attached to it."
However, some observers said there could be broader implications given that Canada is likely to face future requests to repatriate youths sentenced by foreign states for crimes committed abroad.
"This could occur in any context — such as a youth fighting for ISIS or a teenager convicted of a drug-related crime unconnected to terrorism," Hnatiw said.
"The decision will give some direction on how these youths are to be treated by Canada when they are brought home to serve the balance of a foreign sentence."
The Supreme Court has twice before taken up Khadr's case, both times siding with him.
In 2008, the court ruled Canadian officials had acted illegally by sharing intelligence information about him with his U.S. captors.
In 2010, the top court declared that Ottawa had violated his constitutional rights when Canadian agents interrogated him in Guantanamo Bay despite knowing he had been abused beforehand.
In the interim, Khadr is adapting to life outside the confines of a prison, said Dennis Edney, the Edmonton lawyer who has taken him in while on bail.
"Bought him a bike and watched him ride away," Edney said. "Pretty symbolic."
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