As stated in the book, Mr. Walt's wife was extremely good at persuading people and getting to agree with her on mostly everything. So since she was doing a good job at convicing Skiff Miller to give them the dog, Walt didn't want to interfere because if he did, things would not go as expected.
Skiff Miller wanted to take the dog back and go to Alaska with him i guess but to do this he would have to take it from the couple that took the dog in and took good care of it. Skiff Miller must have gotten attached to the dog and felt a sense of love and yeahh
