The lawsuit accused the defendants of committing "acts of unjust enrichment by the unauthorised appropriation of plaintiff's work and the goodwill associated therewith".
Carey previously recalled being taken aback when her record label suggested that she should release a Christmas song.
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The 53-year-old star said: "When I wrote All I Want for Christmas Is You, the label was like, 'okay, why don't you do a Christmas record?' And I'm like, 'Really, now?' Like, second album, two albums in.
"And I was like, 'Well, I do love the holidays, let me try.' So, All I Want for Christmas Is You is the first Christmas song I ever wrote, and then I worked on it with my then-writing partner, Walter A, and we just wanted to make it feel like a modern classic."