BEIJING — A few months after Lu Qiumei gave birth to her daughter in 2012, local officials visited her home and told her that she was required to be fitted with an intrauterine device.

For more than three decades, this was national policy in China. The IUD was the government’s most important tool for limiting couples to one child, and almost all new mothers were required to get one.

Ms. Lu, a former advertising executive, considered the demand invasive, insulting and potentially harmful to her health. Still, like hundreds of millions of Chinese women before her, she made an appointment with a state gynecologist and had one put in.

Now, a year after abandoning the “one-child” policy, the government is hoping to make it up to Ms. Lu and millions of women like her — by removing their IUDs, free of charge. But the offer, made without even a hint of an apology, has provoked incredulous outrage.

“We shouldn’t even have had this in the first place, and now the government wants to use it as a form of state benefit for people,” Ms. Lu, 36, scoffed in a phone interview from her home in the eastern city of Linyi. “It’s like they are slapping themselves in the face.”

While IUDs elsewhere can often be removed with the tug of their strings in a doctor’s office, surgery is usually needed in China because most devices here are designed or altered to be more difficult to extract, some with shortened strings and others with no strings at all.

But many Chinese women have chafed at the thought of the government’s getting involved, yet again, in their private lives. And for many mothers, the offer has come too late for them to consider having a second child.

“It’s the equivalent of someone injuring you and then mending the wound,” said Zhang Xintian, 25, who watched her mother go into surgery two years ago in the eastern province of Zhejiang to remove the IUD she had worn for more than two decades.

In China, women often have the same IUD from soon after childbirth until menopause; while popular IUDs in the United States are typically deemed effective for up to 10 years, those used in China offer birth control for much longer.

China began demanding that women be fitted with an intrauterine device after they had one child, and sterilized after they had two, in the early 1980s. Those who refused risked that their children would be denied access to public schools and health insurance. Civil servants and state employees who refused lost their jobs.

From 1980 to 2014, according to official statistics, 324 million Chinese women were fitted with IUDs. And 107 million underwent tubal ligations or, as is commonly said, got their “tubes tied.” Local officials were evaluated by their ability to meet targets, leading some to order that the procedures — as well as abortions — be performed by force on women who resisted.

Then last year, confronting an aging population and a shrinking work force, President Xi Jinping relegated the one-child policy to the Communist Party’s scrap heap of discarded dogma. And without so much as an expression of regret or an admission that it had perhaps made a mistake, the party pivoted from punishing couples for having a second child to encouraging them to get on with reproducing.

To that end, an official said at a recent news conference that 18 million women would be eligible for the free removal of IUDs in the next three years so they could bear a second child.

“Our country provides support in terms of law, finance and service systems to ensure citizens’ access to the free removal of IUDs,” said the official, Song Li of the National Health and Family Planning Commission’s department of women and children.

But the head-spinning reversal, the paternalistic attitude, the failure to accept any culpability — for some, it was too much. Within hours of the news conference, the internet was fuming with indignation.

The mass implantation of IUDs amounted to “involuntary, forced acts of mutilation,” Han Haoyue, a popular columnist, wrote in a post shared nearly 3,000 times on Weibo, China’s version of Twitter. “And now, to say they are offering free removal as a service to these tens of millions of women — repeatedly broadcasting this on state television as a kind of state benefit — they have no shame, second to none.”

Over the years, many Chinese women have come to hate the IUD, which is inserted into the uterus to block fertilization. In the novel “Frog,” by Mo Yan, the first Chinese citizen to win the Nobel Prize in Literature, the main character imposes a reign of terror involving the compulsory implantation of IUDs and tries to catch women who surreptitiously remove them.

In mainland China, being fitted with an IUD is called “shang huan,” a phrase that literally means “installing a loop,” referring to the low-cost, stainless steel ring that was the state’s preferred device for more than a decade despite higher rates of complications. The rings were replaced in the mid-1990s by safer and more effective IUDs.

According to gynecologists in China, IUDs used for Chinese women were meant to be left indefinitely, with surgery necessary to take them out.

Dr. Gloria Korta, a gynecologist at Winchester Physician Associates in Massachusetts, who toured Chinese hospitals as part of a cultural exchange in 2001, said that while there was a risk of infection from having an IUD implanted for many years, it was small.

Perhaps because of the problems associated with the early model, there remains widespread concern in China about the IUD’s impact on women’s health. In 2012, the online portal Tencent published a lengthy report arguing that many Chinese women had “experienced serious damage to their mental and physical health” from the IUD campaign because of “rough surgeries and poor hygiene conditions.”

Ai Xiaoming, 63, a prominent documentary filmmaker, said many women, herself included, had never been advised of potential complications and the need for regular checkups after getting an IUD. She had to have a hysterectomy when surgery to remove her IUD was botched.

“In the eyes of the government, women are labor units,” Ms. Ai said. “When the country needs you to give birth, you have to do so. And when they don’t need you to give birth, you don’t.”

Even before the end of the one-child policy, the government allowed some women to remove their IUDs if they complained of medical complications. Others, including Ms. Zhang’s mother, did it without permission, paying sympathetic doctors to remove them.

But Wang Feng, a sociology professor at the University of California, Irvine, who studies the one-child policy, said the government appeared to be preparing to remove IUDs on a larger scale.

“They were anticipating the numbers, how many operations need to be done, as if this is another government program,” he said.

The government’s eagerness appears to be driven in part by growing concern over the economic impact of the nation’s plummeting birthrate, now one of the lowest in the world. According to 2015 data, Chinese women had 1.05 children on average, well below the population replacement rate of more than 2.1.

With fewer young people to support larger numbers of retirees in China, scholars have warned of a looming demographic crisis. But many couples are not interested in having a second child, some because of the potential costs, others because of their age.

Cao Cuihua, 35, a restaurant owner in the central province of Anhui and the mother of a 9-year-old boy, said she did not plan to remove her IUD because she and her husband could not afford more children.

“I did think about having a second child, but my economic circumstances don’t allow it,” she said. “This national policy to have two children has come a bit too late.”

Yi Fuxian, a scientist at the University of Wisconsin-Madison who studies China’s demographics, said half of all Chinese women eligible to have a second child were 40 or older.

“Most people have already lost the ability to give birth,” Dr. Yi said by email. “The willingness to have children is already very low, so the Chinese government’s offer of free surgeries will be of no avail. It will have little effect on the birthrate.”

Mao Qun’an, a spokesman for China’s family planning commission, defended the offer to remove IUDs and said the government would also cover the costs of surgery to reverse tubal ligations and vasectomies. (Such procedures are more complicated, and critics say most Chinese hospitals are not equipped for them.)

Dr. Dalice Marriott, a gynecologist at Beijing United Family Hospital, said a woman who had an IUD for a long time ran the risk of “having it embedded in the uterine wall.” “That makes it much more difficult to remove,” Dr. Marriott said, adding that the surgery could result in bleeding, infection and injury to the uterus.

Asked about the public outcry over the government’s offer to remove IUDs, Mr. Mao replied, “We did not deliberately emphasize that it’s a government benefit.”

Li Yinhe, a prominent Chinese scholar of sex and the family, defended the government’s approach, arguing that population control measures were “not targeted against women’s rights.”

“If the state doesn’t engage in this, then it’s not only a disadvantage for men, it also hurts the interests of women,” she said. “Women giving up their reproductive rights is a sacrifice that is made for the whole Chinese society.”

But many women want the government to acknowledge that its original policy was wrong. “What they’ve done to women is inhumane,” said Xu Dali, 35, a mother of two sons in Linyi. “Why did the government force every women then to have an IUD? At that time, why did it not consider the physical harm that has been inflicted on every woman?”