The reasoning behind the 1970 amendment is usually traced to the Nuremberg Laws. Nazi Germany defined a Jew for the purposes of persecution as anyone with a Jewish grandparent. The amendment drew Israel’s circle of protection at the same radius: if having one Jewish grandparent was enough to be persecuted, it should be enough to be given refuge.
From https://masaisrael.org/law-of-return-israel> Converts to Judaism who wish to immigrate to Israel are evaluated on a case-by-case basis by the Israeli Interior Ministry, which determines whether the conversion was sincere in its view