Feinstein's action comes alongside an effort by Republicans to discredit the dossier as a politically motivated document that the FBI has relied too heavily upon in its investigation. Feinstein sought to push back against that perception and to bolster the FBI's credibility.
"The innuendo and misinformation circulating about the transcript are part of a deeply troubling effort to undermine the investigation," she said.
Grassley, who said Feinstein's move "undermines the integrity of the committee's oversight work," had refused requests by Simpson to release his entire 10-hour interview, which was conducted in August.
The Senate committee has been probing how the FBI handled allegations it received from a British ex-spy, Christopher Steele, who compiled a series of memorandums, later collected as a dossier, alleging that the Trump campaign coordinated with the Kremlin — a claim the president has repeatedly denied.
The 312-page transcript shows that Republican staffers on the committee repeatedly pressed Simpson about whether he had political motivations in hiring Steele. Simpson acknowledged that he didn't like Trump as a candidate but said his job was to find facts, not to push an agenda.
In his testimony, Simpson said Steele contacted the FBI with concerns about Russian meddling in early July 2016. When the bureau reinterviewed Steele in early October, agents made it clear, according to Simpson's testimony released Tuesday, that they believed some of what Steele had told them.
Simpson also said Steele was told that the FBI had someone inside Trump's network providing agents with information — a claim he also made in an op-ed for the New York Times last week.
"My understanding was that they believed Chris at this point — that they believed Chris might be credible because they had other intelligence that indicated the same thing and one of those pieces of intelligence was a human source from inside the Trump organization," Simpson said.
Simpson said he didn't know whether the person was connected to the Trump campaign or a Trump company, adding that his understanding was that the source was "someone like us who decided to pick up the phone and report something."
Several people familiar with the probe said Simpson's comments refer to a report from an Australian official who contacted U.S. officials in late July with concerns about a conversation months earlier in London with Trump campaign adviser George Papadopoulos. In 2017, Papadopoulos pleaded guilty to lying to the FBI and is cooperating with investigators.
At another point in the interview, a lawyer for Fusion GPS, Joshua A. Levy, made a jarring assertion: that the dossier's publication had led to someone's death.
"Somebody's already been killed as a result of the publication of this dossier and no harm should come to anybody related to this honest work," Levy said late in the interview, according to the transcript.
Levy did not expand on that claim in the interview, nor is there any public information that would tie a specific killing to the information in the dossier. A person close to the investigation said Fusion GPS has long worried that Steele's overseas sources could be in danger, given a handful of killings that took place in the months after the dossier's existence became known.
Representatives for Fusion GPS declined to comment.
Fusion GPS was hired in mid-2016 by a lawyer for Hillary Clinton's presidential campaign and the Democratic National Committee to dig into Trump's background. Earlier that year, the firm had investigated Trump for a conservative website funded by a Republican donor, but that client stopped paying for the work after it became clear that Trump would win the GOP presidential nomination, according to people familiar with the matter.
After Democrats began paying for the research, Fusion GPS hired Steele, a former senior officer with Britain's intelligence service, MI6, to gather intelligence about any ties between the Kremlin and Trump and his associates.
As the investigation by special counsel Robert S. Mueller III has gathered momentum in recent weeks, Republicans have expanded their attacks on Fusion GPS, Steele and the FBI.
Conservatives have accused the bureau's senior leaders of being biased or corrupt in their handling of investigations involving Clinton and Trump, attacking the reputation of an institution that has long held itself to a standard of being nonpartisan and evenhanded.
Democrats — and even some Republicans — were alarmed last week when Grassley made a criminal referral to the Justice Department, suggesting it investigate Steele for possibly lying to the FBI.
Feinstein countered by releasing the Simpson transcript, a move that at least one senior Republican applauded.
"I think that's a good idea,'' said Sen. John Cornyn (R-Tex.), who said he wanted more transparency on how the FBI gathered information and the extent to which investigators may have used the dossier as a partial basis for obtaining a surveillance warrant.
In urging the committee to release the full transcript of his interview, Simpson has argued that Republicans are trying to obscure what happened in 2016.
Through much of 2017, Feinstein and Grassley made joint requests for information about Russia and the FBI's investigation of election interference. In the fall, however, tensions between the two senators spilled into the open as Grassley requested information from the FBI and other sources without Feinstein's support.
Increasingly, the Democrats and Republicans on the committee are going in different directions, with Grassley moving to investigate matters involving Clinton when she was secretary of state and Feinstein concentrating on Russian interference in the election.
Erica Werner and Rosalind S. Helderman contributed to this report.