Ben,
Assuming you are using the fatfs that comes with TI-RTOS, you can find the source for remove() (which calls the corresponding file driver's 'unlink' handler) in ti/sysbios/fatfs/ff.c. The function name is f_unlink().
After making your changes to ff.c, you'll need to rebuild TI-RTOS to incorporate your changes. The instructions for doing this are in section 8.1.1 of the TI-RTOS user's guide.
Alan