The concern for INZ about an applicant with Hepatitis C is likely to be the potential danger to others, depending on what treatment they have had, how effective it has been, and what the prognosis is, as stated by their specialist. (If you look here
https://www.immigration.govt.nz/opsmanual/#46506.htm, you'll see that Hepatitis C at a particular stage and need of treatment would be cause for refusing a
resident visa.) However, since nowadays the disease can be effectively treated, for people like your mother, it will be a medical that has to be considered by a Medical Adviser (MA), whose job it is to ask whatever questions necessary to get to a clear understanding of the person's
present state. So yes, you're right, you will need to get another set of tests to show her present condition, and a report from the specialist saying what treatment she has had, what effect it has had, and his opinion of the prognosis. INZ wouldn't say someone had an acceptable standard of health (ASH) if they had only just discovered, untreated, Hepatitis C, but a case that has been successfully treated can be accepted.
This page
https://www.immigration.govt.nz/opsmanual/#44856.htm shows you the requirements for a temporary entry class visa.
If the CO has asked for further information by a certain date, and it's unlikely that you'll be able to get the information from the specialist in the time, reply to the CO before the deadline, telling him/her that you've asked for new test results and the specialist's report - maybe even send a copy of whatever you have asked the specialist so they can see you have done as much as you could - and say that you'll send the results as soon as they are to hand. Normally, INZ are all right with allowing extra time when they can see that the applicant isn't just ignoring them, and has done whatever they can so far.