Can I charge my tenant for damage to a carpet?

Maintenance

One of my student tenants damaged the carpet in her bedroom by placing hot hair straighteners on it in several places on different occasions. The carpet was brand new when she moved in last year so this was very aggravating especially as it wasn’t just a one time mistake but clearly happened several times. The tenancy has now ended and I would like to charge her for the carpet - there is no dispute between us that she did it. However she wants to see written proof that I have paid for the work and photographic proof that I have actually replaced the carpet and not just pocketed the money. Does a tenant have the right to insist on this or is she obliged to pay for the cost of damage whether or not the Landlord puts that damage right?