Krause catalog lists two types with madonna/ arms of 1625 NB.
One type has Madonna and titles obverse, arms and mint mark reverse, KM-163: https://www.ngccoin.com/price-guide/world/transylvania-groschen-km-163-1625-cuid-1102030-duid-1548079
https://www.acsearch.info/search.html?id=4246931
The other type has arms obverse and madonna reverse, KM-161. KM does not have an image for this type, so we don;t know where the mint mark appears, and also says variations exist. I cannot find an image online, but maybe someone has a Hungary catalog and can check.
So, I think for now, there is still the possibility the coin is the KM-161 type .
Edit: Having now looked through as many images as I could find for the years 1624-1626, I also agree that counterfeit is possible. I cannot find types in the 1620s that use GABRIEL spelled out completely, or use the shield with curved sides. As you say, legend on the madonna side also does not match in major ways, and the madonna is lacking the normal flames as best I can tell.