Basically いいえ is the negative response equivalent to NO. In your example context, it most likely means NOT AT ALL. However keep it in you mind that answering only いいえ often sounds a little impolite. It should be followed by another phrase.
Lee is right. YOU’RE WELCOM or NO PROBLEM (in this context) is どういたしまして. It’s not that formal, but for some people like me, it sounds a little bit too cliche. In a casual situation, I usually answer だいじょうぶ. Or I just give an affirmative response はい/うん, implying YES I ACCEPT YOUR GRATITUDE.