What caused Aunt Alexandra's "look of pure gratitude" towards Miss Maudie in Chapter 24 of To Kill a Mockingbird?

In chapter 24, Scout attends Aunt Alexandra's missionary circle and listens as the Maycomb ladies talk about J. Grimes Everett's missionary work in Africa and gossip about local news. After Mrs. Merriweather briefly discusses how J. Grimes Everett is attempting to rid Africa of "sin and squalor," she begins discussing how her black maid has been in a melancholy mood ever since Tom Robinson was convicted of assaulting and raping Mayella Ewell. She then begins to indirectly criticize Atticus for defending Tom by saying,

"I tell you there are some good but misguided people in this town. Good, but misguided. Folks in this town who think they’re doing right, I mean. 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. That’s all they did" (Lee, 236).

Miss Maudie immediately comes to Atticus's defense by coldly asking Mrs. Merriweather the following,

"His food doesn’t stick going down, does it?" (Lee, 237).

Shortly after Miss Maudie defends Atticus, Scout notices her aunt give Maudie a look of "pure gratitude" as if she was thanking her for defending her brother. Scout is astonished at the "world of women" as she notices Aunt Alexandra silently acknowledge and thank Miss Maudie for defending Atticus.

Why did Aunt Alexandra thank Miss Maudie silently in To Kill a Mockingbird?

During the ladies social in chapter 24, Aunt Alexandra is barely holding it together.  She is worried about her brother Atticus, and is having a hard time with the hypocritical and racist remarks of others.  When Miss Maudie intervenes, she is grateful to have someone on her side.

She says:

“His food doesn’t stick going down, does it?”

This statement outlines the hypocrisy of those who are willing to enjoy Atticus's hospitality and eat his food, even though they talk about him behind his back.

Scout is surprised that Aunt Alexandra could be grateful for anything.  She is puzzled by what her aunt would thank Miss Maudie for.

She gave Miss Maudie a look of pure gratitude, and I wondered at the world of women. Miss Maudie and Aunt Alexandra had never been especially close, and here was Aunty silently thanking her for something. For what, I knew not.

This is an example of Scout not understanding the adult world.  She doesn’t understand how politeness requires Miss Maudie to say what she means to say indirectly, and Alexandra to thank her indirectly.

They were at the missionary meeting, and Mrs. Merriweather had made some underhanded and very rude remarks about Atticus defending Tom Robinson in the trial.  Here they are, sitting in Atticus's very house, and Mrs. Merriweather has the audacity to say,

"there are some good but misguided people in this town...who think they're doing right...but all they did was stir 'em up."

She is referring to Atticus, who did the right thing to defend Tom Robinson, and how in doing so, it really made all of the black people hopeful, and then when the guilty verdict came down, they were upset with it.  She goes on to say that her own servant, Sophy, was "sulky" and "dissatisfied" because of the result of the trial, and that she had wanted to fire her because of it.  At this point, Miss Maudie interjects icily, "His food doesn't stick going down, does it?" meaning, Atticus's food that at that very moment Mrs. Merriweather was eating.  Miss Maudie was saying that if Atticus bothers you so much, if what he did in helping Tom Robinson-and hence making your slaves unhappy and not as good servants-was so awful to you, why are you sitting in his house and eating his food?  Wouldn't you be so disgusted that you wouldn't want to eat his food?  Wouldn't it stick a little as it went down because you were so disgusted with him?  It pointed out Mrs. Merriweather's hypocrisy; she was bad-mouthing the very person who was helping to make her comfortable at that moment, and didn't even have the guts to mention his name out loud, but instead gave a side-handed insult.  It was like spitting on Atticus's front door and then demanding he feed her.

Alexandra, who had been very offended by Mrs. Merriweather's remark, was relieved that Miss Maudie had stepped in, and with one quick comment, pointed out Mrs. Merriweather's rudeness and vindicated Atticus in one fell swoop.  As hostess of the party, and as sister to Atticus, she was grateful for the help in putting Merriweather in her place.