I heard a story about a sick girl who was cured by Baba. Can you tell me the details from the Satcharita?

Yes, a footnote in Chapter 33 recounts this healing. The story concerns the daughter of Khimji Lalji Joshi, who was so ill and weak that her limbs were like twigs and she had to be carried. Her mother first took some Udi which provided initial relief. They then traveled to Shirdi, where Sai Baba personally applied Udi to the girl and blessed her. As mentioned in the notes for Chapter 33, she began walking on her own within a few days. When she still had trouble getting up and sitting, Baba gave her a fruit to eat, which completely resolved her remaining difficulty.