Last week, employees at T.J. Maxx and Marshalls got very clear instructions about where to put signs for Ivanka Trump products: in the garbage.

The TJX Companies, the retailers’ parent company, told employees not to display Ivanka Trump merchandise separately and to throw away Ivanka Trump signs, according to a note to employees on Wednesday, a copy of which was obtained by The New York Times.

“Effective immediately, please remove all Ivanka Trump merchandise from features and mix into the runs,” the note read. “Runs” refers to the normal clothing racks where the majority of products hang. “All Ivanka Trump signs should be discarded.”

A spokeswoman for the TJX Companies, Doreen Thompson, confirmed that the message had been sent to stores.

“The communication was intended to instruct stores to mix this line of merchandise into our racks, not to remove it from the sales floor,” Ms. Thompson wrote in an email. “We offer a rapidly changing selection of merchandise for our customers, and brands are featured based on a number of factors.”

Ms. Thompson did not respond directly to questions about whether instructing stores to discard signs was unusual. But a worker at one of the company’s stores, who was not authorized to speak publicly, said she had not received such a request during her several years at the company.

Other retailers are also changing their relationships with Trump brands. Moves to pull back from companies associated with Trump products have been applauded by critics of President Trump. Many have called for shoppers to boycott Ms. Trump’s handbags, jewelry, clothes and other accessories.

But the businesses who do pull back also risk attracting other attacks, and not just from customers who support the president. Mr. Trump is not shy about using Twitter to air grievances against people or companies he thinks have treated him unfairly.

On Wednesday, Mr. Trump fired back at Nordstrom, which dropped his daughter’s products from its website last week.

Shares of Nordstrom dipped slightly after the tweet but quickly recovered. The company did not immediately respond to requests for comment.

The president’s statement came after many of his supporters had already begun tweeting #BoycottNordstrom.

In a statement last week, the department store said that its decision had been based on sales performance, not politics. Nordstrom still has Ivanka Trump items in its inventory, which will be sold in some of its physical stores.

A spokesman for the Ivanka Trump brand declined to comment on the president’s Twitter message.

Neiman Marcus has also changed its relationship with the Trump brand, but Ms. Trump’s clothing is still sold at Macy’s, the nation’s largest department store, as well as its sister company Bloomingdale’s, where her shoes and handbags are available online.

In August, Bloomingdale’s committed to selling her clothes in seven of its physical stores, according to a spokeswoman, Anne Keating. Four stores have already started, while Ms. Trump’s products will appear in three more this month and next. Ms. Keating said the company had no plans to expand its distribution.

“I think they all have probably been looking closely at Ivanka’s sales numbers and weighing whether they’re worth all the problems she’s brought them,” said Shannon Coulter, who helped found #GrabYourWallet, an online campaign to boycott Trump products.