Which of the following demonstrates the pattern of development in Greylag Geese?
Your logic seems fine to me.. 

Option B: The hatching at an advanced stage is critical for imprinting.

This is wrong because Konrad Lorenz (who rediscovered imprinting) 


  demonstrated how incubator-hatched geese would imprint on the first
  suitable moving stimulus they saw within what he called a "critical
  period" between 13–16 hours shortly after hatching (reference).


So saying that the hatchling should be at an advanced stage is incorrect.

Option C: The capacity to recognize an adult of its own species is necessarily inherited.

Again this is incorrect because Lorenz has also stated that 


  The human-imprinted gosling will unequivocally refuse to follow a
  goose instead of a human, but it will not differentiate between a
  petite, slender young girl and a big old man with a beard (Lorenz,
  1965) (reference).


Also in this article it is implied that starlings that are imprinted to humans do not relate to its own kind. 

Option D: Rearing by humans does not alter the object of the behavioral routine.

From the earlier findings, this is obviously false. Moreover a duck keeper has explained imprinting thus: 


  An imprinted duck--a duck that was raised from the moment of hatching
  by a human and so views the human caretaker as a parent or equal--may
  become accustomed to riding in the car. Imprinted ducks might go
  camping with you (although you must keep them beside you at all times
  or in a crate) or go on play dates to a friend's house (you will not
  want to take them to a farm or a public pond where they may contract
  diseases). If your duck is in a diaper, you will need to change the
  diaper every hour or so (reference).


This shows clear behaviour changes.

Option A:  Geese reared by humans cannot be taught to respond to its own species.

It is mostly accepted that it is not with Lorenz himself stating that 


  imprinting is irreversible. It is essential in learning that what has
  been learned can be either forgotten or modified (reference).


However there are claims to the contrary nowadays with it now firmly established that filial and sexual preferences are reversible (reference). Another interesting article by the American Psychological Association with a few links you might want to check out. 

In conclusion, Option A could also have its problems with some response to its species possible, but overall it is the most and best plausible answer. 



Dr Lorenz with his imprinted geese. Also a very interesting read (reference)