On a Mac, user settings usually are stored in the defaults database, which is a set of files residing in ~/Library/Preferences and /Library/Preferences. Those files end in .plist. You can display its contents on the command line by entering
defaults read, for example
defaults read com.adobe.reader | less. Searching for RecentFiles may reveal, to a little surprise, two or more data structures. The defaults database is heavily hierarchical; what is stored, and how, depends on the app that makes use of it. It turns out Adobe Reader has individual trees for different versions of the software. So I had entries for version 11 and DC.
The user interface of Adobe Acrobat Reader allows you to clear the list of recent files. However, this seems to have impact on the current version only. Because if I do so, the recent files list of the older version remains untouched. But why keep the settings for the old version at all? At the commandline I can issue
defaults delete com.adobe.reader 11. This rids me of the old waste. The settings for DC are still intact.
To keep the app from storing the recent files lists does not require the commandline. In the Document settings you can just enter
0as the number of recent files.