I don't use Media Center for that purpose, so this may not be a solution, but a possible workaround, Gill:
1. Open Notepad (or any program with a File > Open menu).
2. File > Open and navigate to the file you want to delete.
3. Right click the file, and it should allow you to delete it.
If not, then the file could be locked. Have you checked that WMC is fully closed before you try to delete the files? Another method might be to use safe mode, but it would be a bit of a faff on a regular basis.
Maybe Sandra, or someone else who uses WMC will have some better ideas?