Desposit refund dispute

Tenancy Deposits

Hi. I had a tenant leave today. She admitted damage to a carpet with a rotating drill chuck that has left a large area where the carpet pile has been stripped bare.
I have been quoted £230 to replace the carpet like for like from the same company that installed originally. The carpet was new when the tenant moved into the property two years ago.
She had paid a deposit of £465 which I registered with tenancy deposit solutions (mydeposits). She had rent arrears of £244 which leaves £221. I have refused to refund this amount to cover the replacement of the carpet. She initially agreed to this and signed to say so.
She is now complaining and disagrees with the amount deducted.
What is my position? Is it up to her to register a dispute?