While many buyers praise the company, it has sometimes had a rocky relationship with employees. In 2007, the Equal Employment Opportunity Commission announced that B&H had agreed to pay $4.3 million to settle a discrimination case stemming from claims that the company paid Hispanic employees in its warehouses less than other workers and failed to promote them or provide health benefits.

The first notice to B&H of the latest complaints came on Sunday, when a crowd of about 300 people held a raucous demonstration on the sidewalk outside the store, on Ninth Avenue and 34th Street. While some employees and supporters briefly paraded through the premises, the Steelworkers delivered a letter addressed to the company’s owner, Herman Schreiber, and its chief executive officer and president, Sam Goldstein, asking to be acknowledged as the “sole and exclusive bargaining representative of the employees.”

Ms. Mazzocchi also dropped off a letter addressed to Mr. Schreiber and Mr. Goldstein, asking that they act on complaints that employees had been subject to discrimination because they are Hispanic, had been pressured by managers to sign English-language forms releasing the company from medical claims and had been forced to work long hours in warehouses where emergency exits were blocked and noxious dust appeared to cause rashes and nosebleeds. She said that if she and other lawyers did not receive a favorable reply by Oct. 20, they would file 180 separate claims with the E.E.O.C.

Mahoma Lopez, a co-director of the Laundry Workers Center, an advocacy group that works mainly with low-income immigrant workers, said they had begun meeting last year with B&H warehouse employees. The center’s organizers held workshops in which they instructed workers about their legal rights, he said, and explained that they would have more strength working together than they would as individuals. Eventually, Mr. Lopez said, the center helped the warehouse employees contact the Steelworkers union.

One of the workers who said he had wanted to be represented by United Steelworkers was Mario Baten, 29, who said he had worked for B&H for six years but had temporarily lost his job in 2010 after he collapsed at work. Mr. Baten, who said he had suffered for years from cancer, said through a Spanish-English interpreter he had awoken in a hospital and received documents that had been delivered to him by a B&H manager.

“He sent papers in English that I had to sign,” he said. “I didn’t know what they were saying.”