At meetings and in online forums, patients and staff members have expressed concern about the institution and the way in which it interacts with the health and pharmaceutical industries. The hospital has announced a task force to study its conflict-of-interest policies and said Tuesday in a note to the staff that it would hire an outside law firm to conduct a “focused review” of unspecified concerns that had been raised internally. The leaders said they believed the concerns were without merit.

That uneasiness was reflected at a staff meeting on Thursday, when a pediatric neurologist told the leaders that she was a little embarrassed about the institution even though she is a spokeswoman for Cycle for Survival, a Memorial Sloan Kettering charity that raises money for research. She asked for advice on how to move on, according to several attendees.

Dr. Craig B. Thompson, the hospital’s chief executive, responded that it was important to focus on the cancer center’s dedication to treating cancer, including the rare cancers that are the focus of Cycle for Survival, according to the attendees. Cycle for Survival raised $39 million this year. The hospital spokeswoman, Christine Hickey, said the 2019 Cycle for Survival event was already planned and would proceed.

The fallout has led medical and academic experts to call for tighter disclosure rules on potential conflicts of interest in the cancer research fields and among major nonprofit organizations. Dr. Thompson and Dr. Lisa DeAngelis, acting physician-in-chief, acknowledged the issue of low morale in an email to the staff on Monday.

“We and our board are very aware of the disappointment and distress that many of you are experiencing after recent events at our center,” they said in the memo, which was obtained from hospital staff members. “We share these concerns and are deeply sorry that you feel let down. As your leaders, we recognize that nothing is more important than maintaining the integrity and reputation of MSK and its staff.”

Fund-raising can quickly dampen when charities sustain a reputational hit, said Sophia Shaw, the co-founder and managing partner of Acorn Advisors, which advises nonprofits. “They’re exactly like investors in a for-profit company,” Ms. Shaw said of donors. But rather than expecting a return on investment, donors are expecting a return on the charity’s mission. “If the donor doesn’t feel that their money is furthering that mission, then they could be reluctant to give it away at that time.”

Consultants for nonprofits said major donors were unlikely to be easily rattled by news reports, but that could change depending on what happens next and how the hospital responds.

“Individual funders — and also foundations and corporations — don’t like bad news,” said Richard Mittenthal, president and chief executive of the TCC Group, which advises nonprofits. “And when there’s bad news, there’s always a question of — is there any more bad news?”