Reichu: Misato and Shinji are actually saying, "Itadakimasu". This is another Japanese expression in the vein of "Tadaima" and "Okaeri nasai" -- its layers of significance are completely lost in translation. Apparently, it has its roots in Shinto:
Killing anything for living should be done with a gratitude ... [and] should be kept to a minimum. Modern Japanese continue to place great emphasis on the importance of "aisatsu" or ritual phrases and greetings. Before eating, one should say "itadakimasu", lit. "I will humbly receive", in order to show proper thankfulness to the preparer of the meal in particular and more generally to all those living things that lost their lives to make the meal.Source
