Now, thanks to Ms Band's visit, this historic shul has finally been rediscovered.
She travelled to Segovia, the Spanish city whose spectacular castle inspired Walt Disney to use it in his films, searching for inspiration for a book she was writing.
"I told my husband that after years of dealing with my family tree, bothering so many people, now that we were retired the time had come to travel. I wanted to see the house of my forefather," she said.
A thorough investigation before her visit uncovered evidence that a synagogue operated in Abraham's palace, which is now maintained by UNESCO and local authorities.
She said: "We planned to stay for two days, to see the palace, look for the synagogue and continue our journey. I came with facts from historians in Israel and knew what I was looking for.
"There are testimonials by Abraham Senior describing prayers held in his house, and how he walked to the synagogue. I was determined to find it. But when we got there, we found half the palace had been taken over by the Franciscans and was used as a monastery.
"I entered through a section open to the public which is used as a museum, and asked the woman at the museum shop if she happened to have a book about Abraham Senior. She asked if I knew who he was. I said: 'I am one of his descendants.'
"She whisked me up to the Department of Culture. Everyone wanted to shake my hand. The mayor provided a guide and announced that the whole palace would be open to us. I told the guide I wanted to see Abraham Senior's synagogue. He said: 'I do not believe there was a synagogue, though it is possible he held a small minyan.' But I insisted I had evidence."
Despite bureaucratic attempts to block her search, Mrs Band urged officials to help her find the ancient site.
She said: "Our guide pleaded with everyone and finally received the key, with a warning that no-one must see us. The guides spirited us in through a small back door. Another guide led us into the heart of the building. We came to a large room. On the right was the women's section with Magen Davids. Across from that, the bimah and a place for the Holy Ark. It was as though the last congregants had just departed. Everyone was astonished.
"In place of the Holy Ark there is now an altar and a crucifix. The guide said everything had been kept in its original form, but there were no windows originally. We noticed small vents near the floor. Here, the Marranos prayed without being seen from the street.
Mrs Band decided to do all she could to have the synagogue returned to the Jewish people, rather than under UNESCO control.
"The Franciscans want to take Abraham Senior's palace like they took the other synagogues," she said. "They do not want people to know what is there. I could not keep silent. After returning to Tel Aviv I got in touch with former Israeli president Yitzhak Navon and the historian who helped me.
"This is a story that must be told. We must apply pressure in the highest places to ensure that the synagogue is returned to the Jewish people."
