If you are talking about removing history of files that were edited in the PSE editor (File >> Open Recently Edited File) then the only way I know is by resetting the preferences. See this picture:
However, this will remove all files from the list NOT just a single file as your question seems to suggest.
Right-Clicking and Delete doesn't work in PSE nor does pressing the DEL button.
So there is no solution to your question as far as I can see it.