The relationship "has caused serious questions as to whether or not Mr. Grant should remain as the mayor in town," said Deputy Mayor Jeffrey S. Craig, also a Democrat.
"The concern that I have personally is that there's a perceived conflict of interest when you are spending time with the developer who has active litigation ongoing with the town," Craig said.
The committee could launch a formal investigation as early as Tuesday, when it will publicly discuss the issue for the first time. Grant is not expected to attend the meeting.
Grant, whose term is up at the end of the year, has said he would not seek reelection. He did not return a phone call Friday seeking comment.
Zeck is a principal with NAR Farms L.L.C. and other development firms. He is involved in "millions and millions of dollars worth of projects" in East Greenwich, said Dale Archer, one of two Republicans on the five-member committee. Zeck also holds two alcoholic-beverage licenses in town.
"The mayor took an oath of office. At no time can you compromise that oath," Archer said. "The results can potentially be a huge negative impact for this town."
The nature of the litigation was unclear Friday. A spokeswoman for Superior Court said the court did not have records of a lawsuit involving East Greenwich and Zeck.
Craig and other committee members referred questions about the litigation to Raymond J. Zane, the township solicitor. He did not return a phone call Friday seeking comment.
Zeck appeared before the township's Planning and Zoning Board as recently as Feb. 19 as a representative of Berkley Square L.L.C., according to minutes from the meeting.
Zeck and other representatives submitted site plans for a mixed-use development project. Grant and the rest of the board voted in favor of the proposal.
A year earlier, at a February 2012 board meeting, Grant recused himself from voting on NAR Farms' application to develop a five-acre property, according to the meeting's minutes.
Zeck could not be reached.
In January, Grant caused an uproar when he removed two employees from the township's annual reappointment list.
Some committee members said that caused them to vote unwittingly to lay off the employees, including a part-time police officer who helped arrest Grant when he was caught driving 91 m.p.h. in a 45 m.p.h. zone on Kings Highway. Months of tense negotiations with the police followed, as Grant and others proposed layoffs to close a half-million-dollar budget shortfall.
A few months earlier, after Grant was charged with driving under the influence, some residents and one Republican committee member called on him to resign. Grant pleaded guilty to the DUI charge in April.
Some have stood by him. Among them is Ron Zeck, according to a report in the South Jersey Times of the committee's Aug. 14 meeting.
"Everyone makes mistakes," Zeck said then.
Contact Andrew Seidman at 856-779-3846 or firstname.lastname@example.org, or follow on Twitter @AndrewSeidman.