Why does Attean's grandmother change her opinion about Matt in Sign of the Beaver?

Attean's grandmother changes her opinion about Matt because of the trouble he went through to save Attean's dog. Attean says,

"My grandmother very surprise white boy go long way for Indian Dog...She say you welcome."

Matt had found Attean's dog caught in a white man's cruel trap. He tried to free the panic-stricken animal, but had been unable to, and had badly gashed his hand in the process. Not knowing what else to do, Matt ran to the Indian village for help. Finding that both Attean and Saknis had both gone hunting, he asked for Attean's grandmother in desperation. Attean's grandmother, who, for good reason, hated all white men, greeted him with coldness and suspicion, not understanding his language nor why he was there at the village. Fortunately, Attean's sister was present, and, understanding a little English, translated Matt's words to her grandmother, and begged her to allow her to help Matt save the dog. The grandmother, shocked that a white boy should be so concerned about an Indian dog, relented, but first demanded that Matt stay so that she could tend to his injured hand. Insisting that Matt's hand could get infected if not properly treated, she washed it clean with clean warm water, scooped "a pungent-smelling paste and spread it over the wound," then bound his hand with a clean bandage. The grandmother then gave Attean's sister permission to go with Matt, and the two were able to save the dog.

Two days later, Attean announced that his grandmother had invited Matt to come to the village for a visit. She had been impressed with his obvious compassion for her grandson's dog, and her attitude for the white man in was somewhat softened. Because Matt, in her eyes, took the first step in showing kindness, she was able to look at him at an individual, rather than just as a member of the people who had so hurt her own (Chapter 18 - 19).