Mrs. Pearce is a housekeeper. She's also, like Pickering and Mrs. Higgins, a voice of reason. Heck, if Pickering is the play's father figure, then Mrs. Pearce is its mother figure (which makes Mrs. Higgins the, uh, alternative mother figure, we guess). Mrs. Pearce watches out for Eliza from the very beginning; like Mrs. Higgins, she's used to dealing with Henry Higgins, and she knows he can get carried away with his little projects. After she shows Eliza to the bathroom, she tells Higgins in no uncertain terms: this scheme is ridiculous. She wants to make sure Eliza doesn't get hurt.
Now, you may be wondering why Shaw has all these so-called voices of reasons. Isn't one enough? Well, no. Think of it this way: Pickering represents the fatherly, gentlemanly voice. Mrs. Higgins represents the once hip young woman voice. Mrs. Pearce represents the traditional, motherly, lower-class (we're talking socioeconomic class, here) voice. She has another perspective on the problems of being a woman, one more closely related to Eliza's original situation in life, and it comes as no surprise that she wants to protect the girl.