If you signed an agreement that had the dogs listed as allowed, then you don't have to pay extra.
If the dogs are not listed in the agreement, then you will have to pay.
The courts will look at the agreement, and see that there is no mention of the dogs, then you will be out the court fees as well as the $500. replacement fee for the carpet. You may even be responsible for more fees, depending on the laws of your state.
I have a feeling you are screwed, this maybe one of those life lessons we all hate.
Make sure you have a written agreement with your new landlord, that lists the type, breed, age, and maybe a picture of the dogs. Make sure you have a copy of your agreement.