What incident in the novel convinces Huck that he must get the money back to the Wilks girls?
You can find the answer to this in Chapter 26.
The King and the Duke have convinced the Wilks sisters that they are the girls' uncles, come from England. Because they are pretending that, Huck has to act as their servant at dinner. So Huck has to go and eat in the kitchen with Joanna, the sister with the cleft palate.
While they are eating, she figures out that he's a fake. She accuses him, but her sisters come and defend Huck. When they do this and when they are so nice to him, he starts to feel really bad about letting the King and Duke scam them so he starts to make a plan to prevent it.
I says to myself, this is another one that I'm letting him rob her of her money. And when she got through they all jest laid theirselves out to make me feel at home and know I was amongst friends. I felt so ornery and low down and mean that I says to myself, my mind's made up; I'll hive that money for them or bust.