"Unaltered dogs" refers to dogs that have not undergone any surgical procedures to change their reproductive organs, typically referring to dogs that have not been spayed or neutered. Full definition
The NYC code changes also established «in the joint custody of the city comptroller and commissioner of finance» a city «animal population control fund» consisting of «all moneys collected from the animal population control program», [the license surcharge of at least $ 3.00 for unaltered dogs]... and all other moneys credited or transferred thereto from any other fund or source pursuant to law. (animallawcoalition.com)
To be fair, there are a lot of unaltered dogs who are happy, healthy and do not present any problems to their owners. (puppy-training-solutions.com)
i can't count the number of times i've come across somebody with a young, unaltered dog with behavioral problems who says «oh, it's not a big deal: this behavior [food aggression, object guarding, marking, humping, dominance, fear of other dogs, etc.] will end as soon as we get max fixed.» (btoellner.typepad.com)