It refers to the process of opening a case of MREs, of which there are twelve in a box, then opening up individual MRE packages, and removing the desired items (generally M&M's and other sweets), and leaving the unenticing remainder.
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Woodward and Bernstein's exposé All the President's Men reports that many staffers who had attended the University of Southern California such as Donald Segretti, Tim Elbourne, Ronald Louis Ziegler, H. R. Haldeman and Dwight Chapin had participated in the highly-competitive student elections there.