Landlord is being cagey about registering them - is he not registered as a landlord, is he worried about revenue etc?
Tenants should go straight to the PRTB, even if they're not registered they can still lodge a dispute.
Did the tenants receive written confirmation from the landlord that the cat was allowed or was it just a conversation had? The lease is the only thing binding the tenants and the landlord, if the lease states no pets then it'll be difficult to prove the landlord agreed to the pet as he will most likely lie and say the conversation didn't take place. Also, the landlord can enter the property after giving notice to the tenants, as far as I'm aware nobody else can, unless the landlord's wife is named on your lease as the landlord also, she has no right to be in the house especially without permission from the tenants.