Chairman Trey Gowdy wants to know why the panel has no emails from October 18, 2011, the day the photo was taken as Clinton, then the secretary of state, was en route to Tripoli.
In fact, the committee says it has no emails at all from Clinton's trip to Libya, which occurred just days before longtime Libyan ruler Moammar Gadhafi was killed.
Eleven months later, in September 2012, terrorist attacks on the US mission in Benghazi killed US Ambassador Chris Stevens and three other Americans.
The recent disclosure that Clinton relied on personal emails to conduct government business has breathed new life into the Benghazi panel's investigation, which had threatened to stall amid accusations of partisanship on both sides.
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Clinton is the clear front-runner for the Democratic nomination in the 2016 presidential campaign, but the controversy has upended her careful blueprint for the rollout of her campaign. Clinton had planned to spend March touting her work on women's issues and giving a handful of paid speeches before announcing her candidacy in early April.
Republican House Speaker John Boehner, meanwhile, has not ruled out a vote in the full House to force Clinton to turn over her server, setting up a high-stakes confrontation between the Republican-led Congress and Clinton.
The House Oversight and Government Reform Committee said it will send a letter Friday to the State Department and Clinton formally requesting answers to a series of questions about Clinton's emails.
Gowdy called the Libyan trip emblematic of "huge gaps" stretching for months in documents turned over to the committee by the State Department. "It's not up to Secretary Clinton to decide what is a public record and what is not," said Gowdy, who wants Clinton to appear before his committee at least twice: once to talk about emails and a second time to offer testimony on Benghazi.