Hertz admin fee - still payable if appeal succeeds?

[powe0001]

I've received a bus lane fine notification from Hertz. They have an admin fee which is in their T&Cs, but I am intending to appeal the fine as the evidence is very poor. Does anyone know if their fee will be waived if the appeal is successful? They haven't paid the fine themselves, they have just passed it on to me with a £60 admin charge, halved if paid within 7 days.