Complex sentence: Their version was earmarked for Aguilera's 2010 Burlesque flick, but wasn't used in the movie for copyright reasons though it did leak online in the spring of 2011.
Split into simpler sentences: Their version was earmarked for Aguilera's 2010 film "Burlesque", but for copyright reasons, ended up not being used. It did, however, leak online in the spring of 2011.