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Simple answer: They didn't. If by this you mean, why were the Elites members of the Covenant during Reach, it was because that happened prior to the events of the original Halo trilogy.

(thel and rtas are talking about the covenant at the end of halo 3 and say something along the lines of they can make their covenant strong or pure again... or something like that... kinda implies that they are infact still very much a part of the covenant...)

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