User Agent: Mozilla/5.0 (X11; Linux x86_64; rv:65.0) Gecko/20100101 Firefox/65.0
Steps to reproduce:
"clear data on exit" is enabled, all the relevant boxes therein are marked except "Downloads" and "Saved Logins". In "Advanced", "Restore tabs" is set to "Don't restore tabs after quitting Fennec". "Do Not Track" and "Tracking Protection" always enabled.
I performed a search on Google.com in anonymous mode (not logged into Google, I do not even have an account there), then I "quit" the app (i.e. close).
Google.com remembers my search term and shows it in the search suggestion history (also shows the option "forget history"). This is clearly because Fennec did not clear the data. Only if I delete the local data of Fennec the search history is deleted, but of course this also removes bookmarks, saved logins, plugins etc.
Local data should be deleted on quitting the app, and Google should not remember my history.