By Victoria McGrane And Ryan Tracy 

WASHINGTON--Lawmakers from both parties grilled Treasury Secretary Jacob Lew on Wednesday over whether financial companies singled out by federal regulators for tougher oversight can ever escape the penalty box.

Several lawmakers raised concerns that firms designated as systemically important financial institutions don't have clear guidance from the Financial Stability Oversight Council on what changes they should make to shed the label, which brings with it tougher rules and Federal Reserve oversight.

"There was no intent to create a 'Hotel California' provision," Sen. Mark Warner (D., Va.) told Mr. Lew during a Senate Banking hearing, referencing the Eagles song about being able to "check out any time you like, but you can never leave."

Mr. Lew heads the oversight council, a group of U.S. financial regulators created by the 2010 Dodd Frank law to help prevent a repeat of the 2008 financial crisis. The FSOC has designated four nonbank firms as being systemically important over concerns their failure could damage the financial system. Those designated include the finance unit of General Electric Co. and insurers Prudential Financial Inc., American International Group Inc. and MetLife Inc.

Mr. Lew said the council provides firms with plenty of detail on the risks in their business models and activities that led to the designation. The council provides each firm with an annual review of its designation, during which FSOC could decide to remove the label if a firm has made significant changes that remove those risks, Mr. Lew said.

That review process is "serious and gives rise to the possibility of removing a designation," Mr. Lew said. "Obviously, a firm would have to change the character of the risk it presents in order for that change to be made."

He suggested it is too early in FSOC's life cycle for lawmakers or others to make judgments about whether the council is serious about letting firms out of the designation. "The test will come over time as firms think through what the supervisory process means and make the business judgments as to whether or not they want to change their business to have the annual review reach the conclusion that they should be de-designated," he said. "It was never meant to be a process that only could go one way."

Several lawmakers, including the Senate Banking Chairman Richard Shelby (R., Ala.) and Sen. Elizabeth Warren (D., Mass.), indicated they believe a key part of FSOC's process should be providing incentives to firms to make changes so they're no longer considered systemically important.

Mr. Shelby asked Mr. Lew if he would support adding language to Dodd-Frank to provide a process under which a firm could work with FSOC before a final designation to figure out how to lower risk enough to escape the label. Mr. Lew said no.

The debate is crucial to those firms, including asset managers and other large financial firms that might someday come into regulators' cross hairs.

So far, only MetLife has publicly challenged the regulators' decision, arguing in a January lawsuit that the council "denied MetLife the opportunity to modify its activities to avoid designation."

The other firms that have received the label haven't yet aggressively pushed to have it removed, according to people familiar with the matter.

But The Wall Street Journal reported earlier this month that GE has undergone a change of heart about GE Capital, and that the banking business' commercial lending arm, which at the end of last year accounted for just under half of its $237 billion in loans outstanding, could be next on the block. The company has made no decision about whether or how to dispose of the business, and any move could come in stages.

The company's move has been driven primarily by two factors. One is the fact that the unit's returns are falling, in part because of restrictions that have led it to hold on to more capital and reduce the amount of profits it can share with the parent company.

And secondly, some GE investors remain hungry for a more pronounced shift away from financial services and toward the company's industrial businesses, which could finally lift the company's share price out of recent doldrums.

One person familiar with the matter said that GE's recent discussions about GE Capital haven't centered on its status of systemic importance. The issue could become relevant in the future if the company makes larger changes to the business, this person said.

Ted Mann contributed to this article.

Write to Victoria McGrane at victoria.mcgrane@wsj.com and Ryan Tracy at ryan.tracy@wsj.com

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