The literally means " You don't have to do that." But actually the speaker want to say "That's very kind of you." Traditional Chinese people don't accept other people's kindness immediately, by which they are trying to be polite.

那 怎么 好 意思 呢 = in English will be "Oh, that's so good!"

我知道在国外不会这样说。我现在在教一个外国人汉语，遇到了这句话，不知道该如何解释。 还有Natalie，谢谢你！

How about "that would make me feel uncomfortable"?

人家貌似不玩虚的，一般都说你实在太客气了，或者你实在太慷慨了。