Sen. Elizabeth Warren, D-Mass., is pressing Andrew Puzder, President Donald J. Trump’s nominee for labor secretary, on what he intends to proceed in reassessing a major investment-advice rule.

In a 28-page letter to Mr. Puzder on Monday, Ms. Warren included several questions about the DOL rule, which would require financial advisers to act in the best interests of their clients in retirement accounts.

Mr. Puzder is scheduled for a confirmation hearing on Thursday before the Senate Health Education Labor and Pensions Committee on which Ms. Warren serves.

Among Ms. Warren’s queries: “Will you commit to only reviewing information that is independent and is not funded or otherwise compromised by financial industry players with a vested interest in the findings? Will you also consider the full benefits of the rule for retirees and consumers in addition to any potential costs for the financial industry?”

Ms. Warren is not likely to have enough time during the hearing to get all of her questions answered. She has asked Mr. Puzder to respond in writing by Feb. 21.

The Senate hearing will come a couple weeks after Mr. Trump sent a memorandum to DOL telling the agency to conduct a new cost-benefit analysis of the fiduciary rule to determine whether it limits access to advice for some investors, disrupts the financial industry or could increase litigation for financial firms.

Mr. Trump told the DOL to propose a rule “rescinding or revising” the fiduciary rule, if it found that the rule now in place causes harm to investors or firms.

The applicability date for the current rule is April 10. The DOL has sent to the Office of Management and Budget a proposal to delay implementation — likely for 180 days.

Many Democrats have expressed concern about the nomination of Mr. Puzder, CEO of CKE Restaurants, which runs the Carl’s Jr. and Hardee’s fast food chains. His nomination hearing has been delayed several times while he submitted his background paperwork.

Ms. Warren called into question Mr. Puzder’s ability to protect workplace savings because of CKE’s employee savings program.

“[Y]our company’s retirement plan was riddled with high-fee investments and low participation rates and was less generous than the plans of your peer companies in the fast food industry,” Ms. Warren wrote.

Although the DOL civil service staff can re-launch the cost-benefit analysis of the rule, they can only go so far in amending or replacing it, according to Larry Cagney, a partner at Debevoise & Plimpton.

“The absence of having someone in place who is a Trump appointee will delay reviewing the rule,” Mr. Cagney said. “The career members of the department are capable, smart people but they do need guidance and direction in terms of making policy decisions.”

He pointed to the example of former DOL assistant secretary Phyllis Borzi, who was the mother of the fiduciary rule. She repeatedly asserted that it was crucial to protecting workers and retirees from inappropriate high-fee investments that erode savings.

“The rule was clearly driven by Obama appointees,” Mr. Cagney said.

It’s not clear when Mr. Puzder will get a vote on the Senate floor. Even though his nomination has stalled, he’s likely to get confirmed, just as all the other Trump nominees have been so far. Republicans have a 52-48 advantage in the Senate.

“I don’t see how the Democrats have any chance of sinking this one,” said a financial industry lobbyist, who asked not to be identified.