Thousands of Facebook users in Arizona may have been startled to see a strange warning appear in their social feeds earlier this month.

“Official records show that your voter registration is incomplete,” began the post. “Follow the link below to complete your voter registration NOW!”

But the message didn’t come from local government officials or civic groups that encourage people to vote. Rather, it was an ad from a super PAC supporting President Trump — part of an effort by allies of the Trump White House to mobilize users on Facebook and harness their personal data, in a way that’s left some experts and voting-rights advocates spooked.

The Arizona ad, paid for by the Committee to Defend the President, is one of roughly two dozen such ads that two pro-Trump super PACs have purchased on Facebook over the past five months, according to an analysis of Facebook’s advertising archive by The Washington Post. Some of the ads falsely suggest that Democrats are purging voter rolls; others direct viewers to some version of a voter-registration form, but only after they submit information, such as their names, email addresses and political affiliations.

Responding to an inquiry from The Post, Facebook said this weekend that it was removing four of the voting-related ads for violating its policies. A spokesperson for the tech giant said it would send other ads purchased by another pro-Trump group, Great America PAC, to third-party fact-checkers to verify their assertions about states purging voter rolls.

Political campaigns have long seized on scare tactics to galvanize voters, bombarding them with direct mail or radio and television advertisements in a bid to get them to register, volunteer and cast ballots on Election Day. What makes Facebook different, experts say, are the tech giant’s powerful tools for finding, targeting and engaging narrow communities. At times that capability has come with great controversy — such as the massive privacy breach linked to Cambridge Analytica, a political consultancy co-founded by onetime Trump adviser Stephen K. Bannon, that resulted in a record fine for Facebook.

The power and reach of political ads on Facebook came into sharp relief earlier this month, after former vice president Joe Biden asked the tech company to remove ads from Trump’s reelection campaign because they contained falsehoods about Biden’s ties to Ukraine. Facebook declined, citing a policy that essentially allows politicians to lie, which Democrats deride as a form of misinformation.

In recent weeks, though, Facebook has shown it’s willing to challenge political ads when they’re purchased by entities other than campaigns, including super PACs. And critics contend the voting ads run by Trump’s surrogates cross the line on what’s appropriate and what should be allowed on Facebook in the first place.

Young Mie Kim, a professor of journalism and mass communication at the University of Wisconsin at Madison, said the paid posts were the “best examples” she has seen of ads that “bypass transparency measures by appearing as a public education type of message when in fact the main purpose seems to be data collection.”

Kim called the tactic “data-bait” — harvesting valuable information about a key demographic using “eye-catching, fearmongering content.”

Leaders of the two super PACs defended the ads as serving the joint aims of registering Trump-friendly Americans and garnering their contact information to communicate with them and mobilize them to defend the president.

“The Committee’s primary goal is to help President Trump get reelected, and voter registration is the key,” said Ted Harvey, chairman of the Committee to Defend the President. The ads, he said, were part of the “Great America Voter Drive” launched earlier this year — an effort that aims to “mobilize a conservative army on behalf of President Trump.”

The super PAC’s data scientists decided on a targeting strategy, such as the Arizona-specific message, based on public records and “proprietary data modeling,” Harvey added. Facebook users who clicked the ad and submitted their emails, he said, are added to the group’s distribution list, so they can remain “engaged leading up to the 2020 election.”

But material implying that an advertiser has specific information about a user is a violation of Facebook’s policy against content that “asserts or implies personal attributes,” including race, religion, gender, age, sexual orientation and criminal record, among other details.

Asked Sunday about Facebook’s decision to remove the ads, Harvey suggested the move amounted to voter suppression. “Our ads have been running on Facebook for weeks now, and we’d be surprised and disappointed if Facebook suddenly decided to engage in blatant voter suppression,” he said.

Voting, in particular, is a sensitive issue on Facebook. The company has sought to crack down on posts, photos and videos that seek to suppress voting, a tactic that Russian agents employed in 2016 to dissuade black voters from going to the polls, according to congressional investigators. Facebook has banned some content designed to deliberately confuse voters, including posts and ads that indicate the wrong date of an election.

But critics, including civil rights groups, say the tech giant has taken a too-narrow view of voter suppression. In the case of the pro-Trump super PAC, the ads aimed to bring certain people to the polls — using misinformation about voter suppression — potentially putting them outside the bounds of Facebook’s policies.

Eric L. Beach, a Republican strategist and co-chair of the Great America PAC, said the messaging was part of the group’s strategy, honed since the 2016 campaign, of mobilizing “low-propensity voters.” The committee has been able to capture 30 million pieces of data from such voters, according to Beach, who called the targeting effort a “great niche for us to keep focusing on.”

But data collection stands at the center of the president’s reelection effort, which is mobilizing to be able to email or text anyone the campaign has identified as a supporter. The campaign’s digital director, Gary Coby, is also the CEO of Opn Sesame, a platform for peer-to-peer texting, which some digital strategists believe could play a commanding role in the lead-up to next November.

Recently, Trump’s campaign manager, Brad Parscale, has been touting his team’s success in amassing voter information at Trump rallies around the country. On Twitter, he called a September rally in New Mexico a “data gold mine,” claiming the campaign was able to match 78 percent of the 45,000 people who registered for tickets to its voter file. Thirty-one percent of those people were Democrats, he wrote.

Last year, Parscale told “Frontline” that Facebook’s ad transparency tools were “kind of like a gift,” enhancing the reach of Trump’s views.

A key question is whether that data can be leveraged to reach new voters. Trump’s 2016 victory was sealed by a combined margin of just 78,000 votes in three states — Michigan, Wisconsin and Pennsylvania — making the work of finding new people to cast ballots for Trump, rather than simply motivating his supporters to turn out a second time, critical to his reelection chances.

While super PACs are barred from giving the data they garner to a campaign, the law permits them to sell such information to a campaign for a “usual and normal charge.”

Privacy advocates criticized the ads, some of which ask, “Are you a victim of voter fraud?” and then send users to sites that collect their data.

“It sounds like a technique that’s used by spammers and crooks,” said Bob Gellman, a privacy and information policy consultant.

The Committee to Defend the President stipulates that it may “automatically collect” technical information — such as an IP address, browser type, operating system and time zone — from those who visit the site.

Gellman said the policy — “reserving to themselves virtually unlimited ability to use whatever data they can get from you,” as he put it — was fairly standard. “But that doesn’t mean it’s good,” he added.