Hi Krikor, what method did you use to delete history? Firefox uses history both in the strict sense (URLs of pages you visited = browsing history, URLs of files you downloaded = download history) and in a broader sense (including form field history, search history, cached web content, cookies, etc.).
One way a site could remember your search is if it set a cookie or placed information into local storage on your last visit. When you are on their page, open the Storage Inspector panel (Shift+F9) to see what the site has stored on your current (and potentially previous) visits. You can right-click cookies to delete them. Or to clear all of the site's cookies and local storage data, click the lock icon in the address bar and use the "Clear cookies and site data..." option.
One way Firefox might offer a form fill suggestion is using Form History. The following article has more info on how that works: https://support.mozilla.org/kb/control-whether-firefox-automatically-fills-forms
Does any of that seem to match up with what you're seeing?
