As I understand it, Zera Yisrael(Seed of Israel) IS a halachic concept, applicable to non-jews who are patrilineal descendants of Jews. That is, some forefather along their direct paternal lineage was halachically Jewish, whether it was one generation ago or a descendant of the Bnei Anusim of the inquisition period or anything in between. This can mean they are either direct paternal descendants or it can mean a distant forefather's mother was Jewish. However if the father is not a halakhic jew or paternal Zera Yisrael, the children are not Zera Yisrael.
So if the only Jewish heritage is on your maternal grandfather's side.. Even assuming so far that your maternal grandfather is a halachic Jew... it would at most make your mother a Zera Yisrael, but not you.
I understand there is a lot of debate today, especially in the area of conversion of descendants of Bnei Anusim and other 'Crypto-Jewish' populations, and ESPECIALLY among paternal "half-jews".. whether Zera Yisrael should have a special status for an expedited conversion or even just be fully accepted as Jews. I am not informed enough to speak further on that.
Still, if you are a potential convert with any Jewish heritage, or none at all for that matter, and you seriously want to become an official member of the tribe, you will be more than welcome.