We do a lot of classical recording in various halls. It is always the policy that the producer pays for the tuning unless the hall we are using provides this service as part of the hall rental which again is paid for by the producer.
Most pro studios add this in to their fee structure and don't charge separately for it. the musician or artist is renting the studio for the session and everything in it should be in working order including the piano, drums, amps and microphones.
Maybe your client is upset that this is a separate charge and maybe feels that she will be nickel and dimed to death with small fees on top of the recording charge.
It is your studio and your piano and should be in tip top shape for the recording. I would suggest looking at your fee structure and make the piano tuning charge one that is rolled into the overall fee structure.
There is a studio near here that had a fee structure that was so complicated no one could understand it. There were charges for every variant. Different fees for tracking, different fees for mixdown with and without the artist present, a fee for renting the studio, a fee for renting the drums, a fee for tuning the drums, a fee for rental of the amplifiers, a fee for having extra people in the session, etc. etc. I convinced the owner to set a fee that was reasonable and cut out all the other fees as no one could keep track of them nor understand them. His business has been better since people know that the hourly charge covers everthing,
Hope this helps.
-TOM-