Air carrier Captain reported that after deicing the aircraft they were advised that there was still ice on the aircraft resulting in the Captain taxing back to the gate.

Narrative

After pushback from gate at Omaha the single de-ice truck assigned to our flight took over an hour to clean the jet. When complete de-ice personnel reported the jet 'free and clear of all ice'. After engine start and just prior to taxi I received a call from the lead flight attendant who told me that a passenger at a window seat near the left wing reported seeing ice still on the wing. I taxied clear of the ramp exit and parked the jet at a hard stand location per ATC instruction. I then went back to the cabin to perform a wing check. There was indeed a very noticeable amount of ice remaining on the left wing. I was unable to check the right wing due to significant ice remaining on the right fuselage covering the windows over and by the right wing. As we were now close to 2 hours with the door closed and into Long Tarmac Delay protocol I returned to a gate to offer egress and do another external inspection of the jet. There was significant ice at the left wing root as well as mid chord just outboard of mid-wing. There was also ice remaining at the right wing root and on the right fuselage; as well as the right vertical stabilizer and numerous static wicks. I reported all to operations; we reboarded passengers; pushed again; and had the plane de-iced entirely a second time by a different crew.