Mary Alice doesn't arrive at Grandma Dowdel's house alone.
When she goes to stay with her Grandma Dowdel, she brings her cat Bootsie with her. But her grandmother doesn't allow the cat in the house, and comes up with a rather unorthodox method for making sure that she accepts her new home:
"I rubbed butter on all four of her paws. That's what you do with a cat in a new place. By the time they've licked off all that butter, they're right at home. Works every time." (1.137)
Grandma butters Bootsie's paws so that she doesn't freak out about being in a new place; instead, the cat will be more preoccupied with eating all of that butter.
It may seem like a strange thing to do, especially when you actually try to picture someone rubbing butter on a cat's feet, but it shows that Grandma Dowdel recognizes how out-of-place Bootsie—and Mary Alice—both feel in their new digs. She even says that Mary Alice needs some buttering up, too:
Then Grandma said in a thoughtful voice, "And you better settle in too, girl. Or I'll butter your paws." (1.140)
She doesn't actually mean that she's going to butter Mary Alice's hands. It's just that she wants her granddaughter to get settled in and not to panic over her new situation. She needs to take things slow ("butter her paws") and come to regard this little town as her home.