Well, the Mitigation Specialist is supposed to look into JA's entire life, home, all family, all schools, all doctors, all friends, and anything else, to find out all about her. To find out if she was abused, if she suffers from any mental illness then or now, if she killed kittens or hugged them, if she had any friends, if she harmed friends or helped them, and the list goes on.
Then the Mitigation Specialist is to help the DT in preparing their mitigation procedure, speech, witness for JA, and what to bring to the juries attention. Since we are not finished with whatever will be said on behalf of JA, we don't know how much was found to be helpful. Even if not much was found, hours go into that work, she also has to endure hours with JA, lol.
I have no idea about the hours requested for pay, but she does get paid for her in Court hours too, I'm sure the hours had to be somehow itemized for the Judge's approval. (Side Note: The big cross could go, or at least be tucked inside though. Looks kind of 1980s Madonna Style, even if she means it as a religious symbol.)