Hello Tobias,
I sent you a PM requesting some additionnal info. Since GCG2016 geoid is paid product from BKG, I downloaded the testdaten and created the geoid over this test area and as you can see, placing 2 markers I get correct geoid height as compared with value extracted straight from tif file in GM....
PS. if you have previous geoids referenced to same vertical datum (DHHN 2016), this may be the problem. I had a geoid over NW Deutschland (GCG2016_NW_Originalaufloesung_clp.tif) and for my Testdaten geoid over Ostdeutschland near Poland to work, I had to move the previous geoid out of geoids folder. So as to avoid conflict. see 2nd attachment