The theory behind pet deposits is to protects landlords from the expense caused by destructive pets. I would absolutely NOT offer additional money for an animal that does not pose this threat, especially since the pets were mutually agreed-upon when you moved in.
I would ask the landlord what exactly was the woman's complaint - that the snake LOOKED AT her? Would she have made the same complaint if your parakeet was on your shoulder? You've already made the commitment to keep them in your private space from now on, any other action by the landlord would just be prejudice.