Add schtruck said, the new version allied you to boot to bios, which will allow you to use the psx's built in memory card manager. To make a new memory card, copy one of the ones you have, copy it to a new folder, config FPSE to use it, then use the manager to delete save files from it. Warning, once you tell FPSE to use a different memory card you can't use the original one again unless you choose 'revevert to defaults' - because the default memory card is in a hidden folder and you can't choose it from inside FPSE.
The memory card is located at /sdcard/.FPSE.
You may try searching your phone for .mcd files to see if you have your memory card somewhere else that FPSE isn't using. Search using a file manager like astro.