On March 19, the company told its employees that they would have the three weeks of flex time, but suggested salaried workers could use it to work remotely. “There may be times when you are using this special time but still have capacity to work remotely,” Spectrum said in a memo to the staff. “We certainly encourage and appreciate that; we need you now more than ever.”

In other memos to various Spectrum departments, the company said that roughly 60 percent of call center workers would still need to go to the office, and that people in management roles would be expected in their usual workplaces.

Spectrum has further revised its policy on working remotely since then, said Ms. Blanchard, the company spokeswoman, so that a “significant majority” of office and call center employees are now doing their jobs from home. She would not specify how many are working remotely or when that shift had happened.

The changes have not fully addressed the concerns of rank-and-file employees and executives, some of whom have said that Spectrum was still not doing enough to protect its workers, according to the person with knowledge of the company.

As of Monday, nearly 8,000 people had signed a petition on the website Change.org demanding that more Spectrum employees be allowed to work from home. The petition was posted last month by a person identifying as a worker at the company.

“Our families at home are under mental agony, thinking of us getting exposed to virus at work,” the petitioner wrote under the name Johnny E. “A little flexibility working during this time really helps all. The work we do can be done remotely without any obstacles. We do on-call and work through the nights from home all the time. I do not see a reason why we cannot work remotely during these difficult times.”

Jeanine Ramirez, an anchor at NY1, Spectrum’s local news channel in New York City, said in an interview that the company should allow more employees to work remotely.