In this photo illustration, a container of Johnson's baby powder made by Johnson and Johnson sits on a table on July 13, 2018 in San Francisco, California.

This year was supposed to be a big year for Johnson & Johnson's consumer business, but fresh concern about the company's talc baby powder threatens that.

J&J relaunched its iconic namesake baby product line this summer to reverse a 20 percent sales decline in J&J's baby care unit since 2011. While trusted for decades, the 124-year-old brand had fallen out of touch with consumers, namely millennial moms, who opted instead for cleaner, natural products from trendy upstart brands.

J&J reformulated and redesigned its baby care products and introduced a new line of products made with cotton. Early data suggested J&J's efforts were working. The business posted a 20 percent increase in the third-quarter from the same time last year.

A Reuters report claiming J&J executives knew its talc baby powder contained asbestos caused the company's usually stable stock to fall 10 percent on Friday, shaving nearly $40 billion from its market value. Its shares continued to slide Monday, falling by another 3.8 percent in midday trading.

Reuters said its review showed that from 1971 to the early 2000s, J&J executives, mine managers, doctors and lawyers were aware the company's raw talc and finished powders sometimes tested positive for small amounts of asbestos.

J&J denied the allegation, saying the story was "one-sided, false and inflammatory" and an "absurd conspiracy theory," according to a statement.

The company over the weekend published a point-by-point rebuttal and said it would also start running ads in newspapers and websites, including The New York Times, The Wall Street Journal, Washington Post and NBC.com, that read, "Science. Not sensationalism." J&J also posted a video Monday of CEO Alex Gorsky reassuring consumers that the talc in its baby powder is safe.

But J&J's efforts may not be enough to ease weary consumers. On social media, people shared stories of their moms using J&J's baby product on themselves and their babies, worrying about the effects it may have.

"This does create a cloud of confusion," Jeffrey Sonnenfeld, senior associate dean for leadership studies & Lester Crown professor in the practice of management at the Yale School of Management, said Monday in an interview with CNBC's "Squawk on The Street."

Kristin Lewis, a mom of three young girls in Greenville, South Carolina, said she used J&J's baby powder when her first two daughters were babies to ward off diaper rashes. She chose the cornstarch version rather than the talc formula after researching and seeing concerns online. Eventually, she stopped using it because she didn't see a point, though she still keeps some in her house, she said.

Lewis, 37, hasn't used any of J&J's other name brand baby products on her girls. She said her pediatrician even told her to avoid the lavender-scented products because they include fragrances. Instead, she uses brands like The Honest Company and Babyganics.

"People gave (J&J lavender-scented products) to me for my baby shower and I gave them away to other people," Lewis told CNBC.