LibreOffice Writer has no built-in facility to remove an entry from the Recent Documents list; however, this can be accomplished using the History Master add-on that has been provided by Bernard Marcelly.
The process is as follows:
(1) Download the History Manager extension (currently Version 1.1.1) as a .oxt file
(2) Install the extension in Writer using Tools – Extension Manager
(3) Run the extension using Tools – Add-Ons – History Master : List Handling
The dialogue box includes an option to “Remove selection” that allows a single file name to be removed from the pick list. Other useful options include the ability to remove all the file entries, move individual entries up and down in the list, and set the number of documents that will be listed.
Suppress Recent Document List