If I'm not mistaken, it's douitashimashite : you are welcome/no problem
Additionally, there is "Kochira koso" which means, essentially in this context, "No, I owe -you- thanks." Or there is simply, "Iie, iie." "No, no." As in, "It's no big deal."
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Correct romanization would be 'doumo arigatou'. It's casual way of saying 'thanks a lot'/'thank you very much'.
It means thank you very much. Other ways of saying thank you are: Doumo = Thank you Arigatou = Thank you
どうも (dōmo), ありがとう (arigatō) and ありがとうございます (arigatō gozaimasu) all mean "Thank you."
In polite or foreign company, you would use "arigatō gozaimasu."