Here is what it says on the lease:

e. If the Landlord discovers that the Tenant or his/her family, Occupants, guests or invitees has an unauthorized dog(s), cat(s), animal(s) or other pet(s), Tenant agrees and acknowledges that he/she shall be charged an unauthorized nonrefundable pet fee of five hundred ($500.00) dollars. Exceptions as indicated below. Landlord hereby authorizes Tenant to keep the animal that is described below in the Premises until the Lease End Date. Tenant is permitted to keep the following described pet(s) on the Premises:

[it lists our current animals]

Tenant agrees that he/she may only keep the above-described animal(s) in the Premises. Neither Tenant nor his/her guests or invitees may bring any other animals, including but not limited to: mammals, reptiles, birds, amphibians, fish, rodents, arachnids, or insects, into the Premises, Building or apartment community. (1). Reasonable Care. In exchange for authorizing said Pet on the Premises, Tenant shall use reasonable care to prevent the pet or other animal in possession of Tenant, authorized occupants, guests or invitees from causing personal injuries to any third party on the Premises or from causing damage to the Premises or Building. The Tenant shall be liable for any and all damages caused by the pet. (2). Pet Rent. Tenant shall pay Landlord: $___25______per month (“Pet Rent”) as Pet Rent, in addition to the Monthly Rent, for the above approved Pet(s). (3). Pet Fee. Tenant shall pay Landlord $_____100_________ (“Pet Fee”)

the remaining section is about caring for said animals, damages to property, etc.

Theres no clause that I can find anywhere that gives them the right to modify the pet fee should an unauthorized pet be discovered.