in Ukraine that sounds like Delaityn.
I think there is a town in Ukraine called Deliatyn or Delatyn
as for the time of immigration to Israel, I guess it was after the II World War (many survivors of the Holocaust left Poland shortly following the end of the war)
I have no idea what was the standard procedure for people leaving Poland for Israel at this time - wether they had to renounce Polish citizenship or not
there is also a possibility that Section's ancestor left for Isreal straight from Germany where they were liberated
I think the OP needs to hire someone (preferably a lawyer with an experience of searching archives) to trace for documments in Poland - but maybe someone can come up with an idea which institution the OP can directly turn to to arrange for an archive query