What to reply to a person saying "Good Morning" when my time zone is different?

The person saying the greeting is wishing something good for the other.

So if it's morning where you are, I should wish you a "good morning", regardless of my local timezone.

Likewise, if it's afternoon where I am, you should wish me a "good afternoon", regardless of your local timezone.

However, if they're already greeted you but used the wrong part of day, it doesn't really matter, the intention is the same. I would still reply with the appropriate greeting for their local timezone.

If someone greets you according to their time zone like good morning/evening/afternoon, I think we should wish them the same, rather than explaining them the time zone difference. These would also make them feel comfortable that there is no gap between you people.

If you are on formal terms with the other person, it would be appropriate and necessary to respond with "Good morning". The idea is to respect his gesture of wishing you, in the first place, rather than distracting from it. Also note the pronunciation, your stress will be on Good, to show that you care more about that part of the greeting :).

I believe this may also apply in an informal case, though I am not sure.