The move came a day after the Flames made headlines by signing restricted free agent forward Ryan O'Reilly to an offer sheet. The Colorado Avalanche, who own O'Reilly's rights after his entry-level deal expired last summer, quickly matched it.
Colorado chose not to take Calgary's first- and third-round picks in the 2013 NHL draft as compensation if O'Reilly went to the Flames.
Calgary acquired McGrattan on Thursday in a trade with Nashville. The Flames gave up defenceman Joe Piskula in the deal.
McGrattan, who played 34 games for Calgary in the 2009-10 campaign, played two games with the Predators and six games with AHL Milwaukee this season.
Aliu played two games for the Flames on his callup and registered 10 penalty minutes.