According to the article, the blogger criticized the congressman for his "childish approach" towards governing.
Of course that's the rub. The article and the Slashdot summary misrepresent the complaint that is in the letter. It is actually about the Political Committee the woman organized to raise funds to support election campaigns. And while she is referred to here as a blogger, she was a former employee of the Republican National Committee. One of the things Congressman Grayson points out in his letter is that it seems a bit disingenuous of her to claim to just be a "private citizen" unconnected with any other political organization when she formerly worked for the RNC.
Further, the fraud he accuses her of is related to raising money for supporting a candidate in an election. Her claim to be his constituent is criminal, not because she is criticizing him, but because she is using it to raise money for an election campaign. At least that is what the congressman is asserting. Further, despite what the summary indicates, it is not his only or even his chief complaint. Rather the chief complaint is that she claims that her organization is a PAC (and raises money for multiple candidates in several campaigns) but in fact appears to only be concerned about one campaign. This would effect who could donate to her committee and how much. It is certainly not a trivial accusation, and there are really laws that govern how much money you can contribute to politicians and political committees.
Whether Congressman Grayson's accusations have merit or it is all a ruse to silence a vociferous critic, I can't say. But I'm very leery of anyone who starts down the path of criticizing someones actions by first misrepresenting what they were. (Why didn't the submitter include a link to the letter [primary source] as opposed to, or at least in addition to, a rather opinionated report on it?)