Wells Fargo & Co.’s political problems continue to mount.

In a letter Thursday to Wells Fargo’s chairman, Sen. Elizabeth Warren (D., Mass.) asked the directors whether they had sufficiently questioned Timothy Sloan about his knowledge of the bank’s sales-tactics scandal—what he knew and when he knew it—before he was appointed the new chief executive officer.

The letter, co-written with Sen. Robert Menendez (D., N.J.), also asked whether Mr. Sloan’s predecessor, John Stumpf, would receive any retirement benefits after abruptly leaving the bank earlier this month.

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