This occurs during the Missionary Circle tea, which Alexandra is hosting in Atticus's house. Grace Merriweather, "the most devout lady in Maycomb," has dominated the meeting from the start, and she has gone from praising the efforts of the group's missionary in Africa to criticizing the Negroes in her own town. She goes too far, however, when she blames Atticus (without mentioning his name) for stirring up the local Negro populace by his spirited defense of Tom Robinson.
"... there are some good but misguided people in this town... Now far be it from me to say who, but some of 'em in this town thought they were doing the right thing a while back, but all they did was stir 'em up." (Chapter 24)
Although Alexandra lacked the nerve for a proper comeback, Miss Maudie didn't. Her response,
"His food doesn't stick going down, does it?" (Chapter 24)
refers to the fact that Mrs. Merriweather is happily eating the food paid for by Atticus in Atticus's own home, yet she has the nerve to criticize him under his own roof. Alexandra's "look of pure gratitude" was her way of thanking Maudie for sticking up for her brother.
She gives her a look of pure gratitude because she defended Atticus and because she accuses the other ladies who thinks the way she does of hypocrisy .