At the time of the attack, Bill Grueskin was working for The Wall Street Journal in the World Financial Center across the street from ground zero. He still has not forgotten how the streets were enveloped in a cloud of ghostly smoke. To make matters worse, Mr. Grueskin was living just down the street in Battery Park City then. So for him, the experience was total — no escape.

“The fact is, I’d like to see the museum,” said Mr. Grueskin, who is now a dean at the Columbia Journalism School, “but I’m not sure I can do it surrounded by people who didn’t go through what I went through. I’m not saying I deserve it, but I’d really like to see the place in private. I just can’t bear the thought of being there with all the buses and tourists in silly hats.”

This week, some of the victims’ relatives appeared at the memorial to protest a decision by officials to transfer the unidentified remains of some of those who died from the Manhattan medical examiner’s office to a specially built repository under the museum. Almost from the moment that the plans for the museum got underway, the families have differed with one another about its purpose and design. Some have even differed among themselves.

“My family is a mixed bag,” said Kathy Bowden, whose brother, Thomas Bowden Jr., died in the attack. “I’m open to it. It hurts to see it, but it also, for me, soothes the hurt a little each time. My husband hates the museum. He hates the idea of having a place, because he hates the idea that 9/11 even happened.”