She should still pay the bill for the tiling and then she would have to argue that you scratched the hob. If she withheld payment that would go against her in court and she wouldn't even be able to start a claim regarding the hob.
I'd go through the legal channel, it is setup to protect you if she withholds the payment.
Customer are not allowed to do that. If they have a problem with something they have to pay you in full and then give you the chance to rectify the problem once it has been rpoven it is your fault.
If the hob is brand new and she has a recent receipt, then perhaps then you'll struggle to defend, otherwise it's a used hob and could have scratches on it.
That said, if a customer is claiming something, I'd try to sort the problem out either way. Though only after payment has been made in full. Just for the sake of keeping your reputation and trying to please the difficult customer.