Mr Justice Mostyn said the woman had also been unable to name any of the evangelists - gospel authors Matthew, Mark, Luke and John.
He said the woman's claim to have converted to Christianity was "hard to believe".
Detail has emerged following a private hearing in the Family Division of the High Court in London.
The judge said he had examined legal issues relating to the woman's children.
He has outlined background to her asylum claim in a written ruling on those issues.
Mr Justice Mostyn said Home Secretary Amber Rudd had refused the woman's asylum claim.
He said the woman, an ethnic Bedouin, had launched an appeal against Ms Rudd's decision.
The judge said reasons why Home Office officials had refused the woman's asylum claim had featured in evidence in the case relating to her children.
He said a Home Office official had "comprehensively anatomised" the woman's asylum claim.
"The official has demonstrated why in numerous respects the (woman's) credibility is fatally compromised," said Mr Justice Mostyn.
"For example, he demonstrates that the claim that the (woman) had become a Christian convert is hard to believe in circumstances where she does not know the name of any of the evangelists, and has no idea what Easter is for or about."
The woman had said she was not safe in Israel and made allegations about members of her family.
She said she had been "grossly mistreated" by her father and brothers.
She said such behaviour was endemic in her culture.
And she said Israeli authorities turned a blind eye to "honour violence" meted out to Arab citizens.
Home Office officials had concluded that there was "ample legislative protection" for women in danger in Israel.
Mr Justice Mostyn said he had analysed issues relating to what should happen to the woman's children - twins now seven who were also in Britain.
He said he had decided that the children should return to Israel with their mother if her appeal against asylum refusal failed.
The judge did not name the children.
