The Bloomberg administration announced last week the search would begin again Monday in a 10-week effort to sift through nearly 600 cubic yards of material only recently removed from the Ground Zero site.
Members of 9/11 Parents and Families of Firefighters and WTC Victims told NY1 they were worried about allegations the medical examiner's office had mishandled DNA evidence in multiple cases.
The organization demanded the effort be delayed until an independent monitor could be installed to oversee the process.
"We want the mayor to come in, appoint an investigator general. Let's get the [Joint POW/MIA Accounting Command] people from Washington, the federal people who do this for the war heroes, let's do it for our heroes who died on 9/11," said Jim Riches, whose firefighter son died while responding to the attacks. "A thousand families have nothing, and we would like to see them all recover something."
Others view the city's efforts in a more positive light.
"It's refreshing when you think about a government office or department like the medical examiner to be so caring and compassionate and dedicated to their continuing efforts to identify other victims," Mary Fetchet, who runs the support group Voice of September 11 and whose 24-year-old son Brad died in the attacks, told WNYC.
Many families have offered the medical examiner personal effects such as toothbrushes or combs in the hopes their loved one will be identified, unlike the 27 individuals whose remains have been found but don't match any of the known victims.
But others, such as Families of September 11 chairman Donald Goodrich, whose 33-year-old son Peter died on United flight 175 when it crashed into the South Tower, say they would rather not know if their family members are identified.
"For me at this stage, it's of no importance to me that somewhere in the city of New York there are bits of the physical being that was once Peter," Goodrich said. "They're there, that science can detect them and then inform me of their detection, is of no solace to me."
"There's nothing modern science can do to test for his soul," Goodrich said. "That belongs in another sphere, and that's what's most important to me."
The city has identified remains of 1,634 people who died in the Trade Center towers. Some 2,753 people died in the attacks.