They are required by law to provide you with an itemized receipt of the damages.

>If the landlord keeps the security deposit to pay for damage, the landlord must provide an itemized statement of costs. The statement must include supporting documentation. The landlord may provide an estimate. If an estimate is provided, the landlord must notify the tenant (in writing) when the repairs have are complete. This notice should include final invoices for repairs. If the final cost is less than the amount of security deposit withheld, the landlord must return the excess to the tenant. The excess must be returned within 30 days after the repairs are complete. 

So they can't just claim a number. And when they provide an invoice - it should have receipts attached for the replacement carpet and installation. Not just what they say it cost - but an itemized cost.

Also - The landlord can only charge for physical damage beyond ordinary wear and tear. This is a common sense rule. For example, if the carpet is worn through proper usage, then this is ordinary wear and tear. If a rug is stained with ink, then this is not ordinary wear and tear. If there is no visible damage in photos, then they can't claim otherwise.

Finally, if the landlord withholds any part of the security deposit, the landlord must send to the tenant, by first class mail, to the tenant’s last known address, a written list of the damages the landlord claims, together with a statement of costs the landlord has actually spent to make the repairs. If the landlord fails to do this within 45 days after end of the lease, the landlord loses the right to keep any part of the security deposit for damages.