If you’ve been carrying out any dodgy searches in Incognito Mode in the iOS 7 version of Google Chrome, you may want to wander casually into settings to delete the search history (looking toward the sky and whistling helps): it appears that Incognito Mode currently isn’t. All searches performed in the private browsing mode are available in search history once you return to normal browsing.
The above video is rather swift, and has no commentary, but what it shows is erasing history to start with a clean slate, entering Incognito Mode, visiting a website, returning to normal browsing and then viewing search history at Google – where the supposed private web session shows up.
Note that you do need to visit Google to see the history: it doesn’t show up when simply using the combined URL/search bar.
Google updated the app last month. The company has not yet made any statement on the bug.