Schumer wants the Department of Homeland Security to test surveillance equipment at the site, survey the perimeter for possible points of illegal entry and check how security guards are performing.
David Velazquez had been security director for The Durst Organization, which took over security of the tower in January.
Andrew Rossig, 33, James Brady, 32, Kyle Hartwell, 29, and Marco Markovich, 27, were arraigned on charges of burglary, reckless endangerment and misdemeanor jumping from a structure, police said.
Three of the four men accused of jumping from One World Trade Center in September 2013, were in police custody on Monday, just days after a New Jersey teenager was caught sneaking up to the spire.
The Bergen County United Way has rallied support and special donations for a formerly homeless Good Samaritan from Hackensack, N.J. who was stripped of his benefits.
James Brady found $850 on a Hackensack sidewalk last April and turned it in to police. Brady was awarded the money six months later, when no one contacted police during the required six-month waiting period.