I was looking for maps for you yesterday that would clarify my explanation but didn't find a useful one.
I was also trying to find the location of the service center that you mentioned but no luck.
There is an information desk in terminal 3 landside, to the left, straight after you exit the luggage collection area/customs.
I sort of assume that this is the service center that the Copenhagen Card website mentions.
If you don't need the information straight away, I'll be in the airport on the 22. of January and I can ask that information desk if they are the picking up point in the airport.