After Mr. Force spent some time on a Facebook page belonging to Hamas, the family agreed to sue. The lawsuit fit into a broader effort by the Forces to limit the resources and tools available to Palestinian groups. Mr. Force and his wife allied with lawmakers in Washington to pass legislation restricting aid to the Palestinian Authority, which governs part of the West Bank.

Their lawyers argued in an American court that Facebook gave Hamas “a highly developed and sophisticated algorithm that facilitates Hamas’s ability to reach and engage an audience it could not otherwise reach as effectively.” The lawsuit said Facebook’s algorithms had not only amplified posts but aided Hamas by recommending groups, friends and events to users.

The federal district judge, in New York, ruled against the claims, citing Section 230. The lawyers for the Force family appealed to a three-judge panel of the U.S. Court of Appeals for the Second Circuit, and two of the judges ruled entirely for Facebook. The other, Judge Robert Katzmann, wrote a 35-page dissent to part of the ruling, arguing that Facebook’s algorithmic recommendations shouldn’t be covered by the legal protections.

“Mounting evidence suggests that providers designed their algorithms to drive users toward content and people the users agreed with — and that they have done it too well, nudging susceptible souls ever further down dark paths,” he said.

Late last year, the Supreme Court rejected a call to hear a different case that would have tested the Section 230 shield. In a statement attached to the court’s decision, Justice Clarence Thomas called for the court to consider whether Section 230’s protections had been expanded too far, citing Mr. Force’s lawsuit and Judge Katzmann’s opinion.

Justice Thomas said the court didn’t need to decide in the moment whether to rein in the legal protections. “But in an appropriate case, it behooves us to do so,” he said.

Some lawmakers, lawyers and academics say recognition of the power of social media’s algorithms in determining what people see is long overdue. The platforms usually do not reveal exactly what factors the algorithms use to make decisions and how they are weighed against one another.

“Amplification and automated decision-making systems are creating opportunities for connection that are otherwise not possible,” said Olivier Sylvain, a professor of law at Fordham University, who has made the argument in the context of civil rights. “They’re materially contributing to the content.”

That argument has appeared in a series of lawsuits that contend Facebook should be responsible for discrimination in housing when its platform could target advertisements according to a user’s race. A draft bill produced by Representative Yvette D. Clarke, Democrat of New York, would strip Section 230 immunity from targeted ads that violated civil rights law.

A bill introduced last year by Representatives Tom Malinowski of New Jersey and Anna G. Eshoo of California, both Democrats, would strip Section 230 protections from social media platforms when their algorithms amplified content that violated some antiterrorism and civil rights laws. The news release announcing the bill, which was reintroduced on Wednesday, cited the Force family’s lawsuit against Facebook. Mr. Malinowski said he had been inspired in part by Judge Katzmann’s dissent.

Critics of the legislation say it may violate the First Amendment and, because there are so many algorithms on the web, could sweep up a wider range of services than lawmakers intend. They also say there’s a more fundamental problem: Regulating algorithmic amplification out of existence wouldn’t eliminate the impulses that drive it.

“There’s a thing you kind of can’t get away from,” said Daphne Keller, the director of the Program on Platform Regulation at Stanford University’s Cyber Policy Center, “which is human demand for garbage content.”