The company behind the anti-Trump intelligence dossier that rocked last year’s U.S. election is mounting a legal challenge to block lawmakers from getting access to its banking records.

Fusion GPS filed a complaint Friday in federal court to prevent its bank from turning over records subpoenaed by the House Permanent Select Committee on Intelligence

The committee subpoenaed Fusion’s banking records on Oct. 4 in an effort to determine who financed former British spy Christopher Steele’s work to write the dossier during the summer and fall of 2016, a source with knowledge of the situation told The Washington Times.

The subpoena, a copy of which is included among the documents filed in U.S. District Court for the District of Columbia, requests documents dating back to August 2015 from the company’s bank — including records of current account balances and past transaction activity.

Fusion, headed by former Wall Street Journal reporter Glenn Simpson, has resisted numerous efforts this week by congressional investigators to obtain more information about the dossier as they probe Russian interference in the 2016 presidential election and any possible coordination with members of the Trump campaign.

Company officials invoked the Fifth Amendment this week rather than testify on Capitol Hill about Fusion’s role in commissioning and compiling the dossier. The company has also refused to hand over certain documents to the Senate Judiciary Committee citing its First Amendment rights.

The general counsel for the House of Representatives filed a motion Saturday to intervene in the Fusion dispute, writing that “the key” to answering a number of outstanding questions about the dossier lies with information held by Fusion.

The committee has sought to understand “all facets of the ‘dossier,’” including who paid for it, any steps taken to collaborate its allegations, and the degree to which the FBI relied on the dossier as part of its own investigation into Russian interference, wrote General Counsel Thomas G. Hungar.

“The records sought by the subpoena will allow the Committee to fully understand and perhaps conclusively determine who paid for the ‘dossier’ and the amount of funds that Fusion GPS paid to Mr. Steele for the performance of his work, as well as determine whether Fusion GPS engaged in other Russia-related work within the scope of the Committee’s pending investigation,” Mr. Hungar wrote.

“Such information is crucial for the Committee to fully investigate not only the ‘dossier’ and its relevance to the question of whether there was possible ‘collusion’ between the Russian Government and the Trump campaign but also other aspects of the Committee’s investigation.”

The bank currently intends to comply with the subpoena by 9 a.m. Monday unless the court intervenes.

The House Intelligence Committee has been unable to verify any of the major allegations that Mr. Steele made in the dossier against Mr. Trump and others. The 35-page document purportedly found evidence that the Russian government had damaging financial and personal information on Mr. Trump that could be used to blackmail the then-Republican presidential candidate.

Intel Chairman Rep. Devin Nunes previously stepped back from the committee’s investigation into Russian interference because of an ethics review into his handling of classified information, and Fusion GPS argues that the chairman’s subpoena violates his recusal from the probe.

The company’s lawyers have asked the court to declare the subpoena “unauthorized, invalid, and not a legitimate legislative activity” and to enjoin the unnamed bank from releasing the company’s financial records to Mr. Nunes, California Republican, or the committee.

In court filings, they said the broad subpoena for all Fusion banking records violates financial privacy laws. It would result in the committee receiving the identities of every Fusion client over the past two years. These would include the clients who financed Mr. Steele’s investigation.

“The Trump Dossier appears to have deeply upset President Trump and some of his allies, including Mr. Nunes, who served on President Trump’s campaign,” one Fusion filing said. “The purpose of the subpoena is to obtain Plaintiff’s entire confidential list of clients and contractors—regardless of any nexus to the ‘Russia investigation.’”

The filings did not disclose the bank, which was referred to as “John Doe Bank.”

The mystery over who, or what organization, financed the dossier has not been solved. Reports indicate that Fusion GPS was commissioned by a third-party to conduct political opposition research on Mr. Trump in the fall of 2015, but that the party withdrew from the contract in the spring of 2016. A different client is said to have taken over the contract with Fusion to continue to research.

Fusion argues that if the bank were forced to disclose its financial records, it “would reveal the identities of all of Plaintiff’s clients, contractors and vendors, most of whom have zero relevance or pertinency to HSPCI’s ‘Russia investigation.’”

The company said it guarantees client confidentiality and a breach such as the one sought by Mr. Nunes would greatly harmed its business.

In one filing, the attorneys seem to indicate that only one entity bankrolled the project.

“The identity of the client who paid for opposition research on Mr. Trump is not relevant to the investigation, and disclosure of every single one of the firm’s clients over the past two years certainly has no possible relevance to the investigation,” the court document states.

But in other filings, the attorneys referred to “clients.”

Fusion is run by former Wall Street Journal journalists, including Mr. Simpson, who circulated the dossier contents among liberal reporters during the campaign, and Peter Fritsch.

Mr. Fritsch signed a court declaration that said, “As a result of the publicity around the Trump Dossier, Fusion GPS has been the subject of extensive and inflammatory media coverage. It has been maligned in the media as ‘a disinformation firm,’ as improperly receiving money from Russians, as a professional smear organization, as partisan operatives, and far worse. The organization and its principals have received threatening communications, including death threats.”

He also said, “Our financial information is intensely private and confidential, as are the identities of our clients. Requiring us to reveal this information would chill our and our clients’ First Amendment.”

Mr. Fritsch and another partner, Thomas Cantan, invoked the 5th Amendment when called to testify on Wednesday before the House committee.

House Democrats have freely repeated in public the dossier’s unverified allegations against Trump and his people. They are fighting all Republican efforts to find out who financed it.