I would respond by saying their “invoice” is unresponsive and to provide an itemized invoice showing the charges incurred for carpet cleaning including the company they hired, date of service, and the charges for cleaning service. There’s no way a carpet cleaning cost $900. It’s up to them to provide evidence as to why they needed to withhold over $900 from you.

First ask for an itemized invoice for charges related to repairing the issue. Normal wear and tear is standard and acceptable. Hopefully you have some pictures of the condition you left the apartment when you left.