Do you mean the drop-down Combobox list for the "Base Path" field?
The ability to remember those paths was only added in January.
23.0.94 (1/12/2018)
7. NEW: The base path of the Rename, Move, & Copy Files dialog is a combobox that remembers the last entered paths.
Have you been changing the Base Path a lot, or not using the directory rule to set sub-paths? I muck around on my test system a lot, and I've still only got seven Base Paths remembered.
I would have expected that if there were too many Base Paths already listed that a new Base Path would replace one of the old ones in the list. Maybe JRiver didn't code it that way... I just did some checking, and I see what you mean. MC stores up to ten (10) Base Paths in the Combobox, and then stops adding any more.
I think that should be fixed. MC should store up to a set number of paths, and then drop off older paths as new ones are added. Or maybe better yet, it should be possible to delete unwanted paths from the Combobox.
Anyway, the only way to remove paths from that list that I currently know of is to edit the Registry. If you are confident in editing some complex values, then you will find the remembered paths in;
Computer\HKEY_CURRENT_USER\Software\JRiver\Media Center 24\Properties
and Value Names;
"Rename From Info - Current" for the current preset or settings
and
"Rename From Info - Presets" for all saved Presets.
Both of those are long strings with carriage returns included, which means that editing them in Notepad or similar and saving them back into the settings doesn't work easily. But I was able to edit out all by two Base Paths in situ in the Registry, so it can be done and works. I only edited the "Rename From Info - Current" setting, so my Presets needed some fixing afterwards.
Just check any Presets, if you use them, after you edit, fix the Base Path, and save them again.