"Have you been surprised by how formalized this network was?" asked Attkisson.
"Yeah, I could not believe it," Sokolow said. "It turns out there was a whole system in place. This Saudi Committee would provide lists of terrorists and their families, all sorts of information, to the bank. The Saudi Committee would advertise throughout the West Bank and Gaza that if you want to contribute funds, to help the families of suicide bombers, you can do so by sending us money via the network of branches of our bank and perhaps others.
"It was just shocking to read this and it was done out in the open."
None of the banks would talk on camera. They say they merely conducted routine banking activities not intended to promote terror.
Credit Lyonnais called the allegations "baseless and absurd."
Arab Bank says it "abhors terrorism." It reportedly admits transferring $90 million in what it calls "humanitarian aid" to Palestinians, but says there was no conspiracy to subsidize suicide bombers.
When asked how big of a deal this lawsuit represents, CBS News analyst Juan Zarate (who was the Treasury Department's assistant secretary for terrorist financing under President George W. Bush), told Attkisson, "I think this is a set of cases that are incredibly important, not just for the banking community but also for the counter-terrorism world, because it potentially sends a chilling signal to banks around the world that they run the risk of financial and legal liability if they're doing business with terrorist actors."
"From the bank's viewpoint, the bank may say we didn't know what they were doing. We're simply doing business with a customer," said Attkisson.
"They knew," said Eugene Goldstein. "They had to know. They could not be in business if they didn't know. They didn't become bankers of that magnitude by being stupid. The money that's funneled there to commit terrorism in that part of the world can just as well be done to promote terrorism in this country and finance terrorism in this country. So they have to be stopped."
Mark Sokolow added, "It should be important to every American to try to put an end to the funding of terrorism, which we've all seen can actually happen on American soil as well."