Since you're not legally a party to the lease/rental contract, you don't owe anything to them!
I wouldnt pay.They knew you had a cat,hadnt let the place in pristine condition when you first rented,and were already told there was no problem.On top of which they cant be bothered to give you a breakdown.On their bikes!
Take it to a civil lawyer..
Press the issue. Hopefully you took pictures prior to moving in.
Pay up b i. T. C h