As Uber struggles to rebuild its management team and board, its leaders are snuffing out internal fires too. One of the biggest: turmoil within its 2,000-person engineering team, the center of Susan Fowler’s now famous sexual harassment and bullying allegations.

In the hotseat is CTO Thuan Pham, who Ms. Fowler said failed to act on her complaints about being bullied by her boss and blocked from transferring teams. While an external investigation cleared him, several rank-and-file Uber engineers on Wednesday and Thursday sent emails to groups across the organization, calling for Mr. Pham to step down because he was named in her post. And on Twitter, Ms. Fowler retweeted a comment asking why Mr. Pham was still at Uber.