I notice in Geany 1.27 (Mint 18.1 repo) it doesn't save search terms. Which is fine, especially between sessions.
In Geany, I take it there's also no "clear recent documents?" (you can set the # of listed recent docs in the config file).
I don't know if it's designed never to save search or "find & replace" history, or if I edited some file and don't remember it. There definitely aren't any menu or prefs for "don't save search history" - or such.
There are no settings in any Geany files to control any of this, that I see. It's OK - I'm just surprised. Most apps save some history and you have to find a way to delete it, if need to. If I edited something in Geany's files to not save search history and forgot what I did, I'd like to see if there's a way to apply it to Mint's text editor.
In Linux Mint, the default text editor is XED. I could easily change it to another editor - even Geany, that doesn't save search history or can clear it. XED has no preferences to not save history; no way to clear it.
XED's Search & "replace with" terms are stored in a binary file - "user." The only way to delete those entries is using the tool, dconf-editor, which isn't that convenient on a regular basis.