Well actually no
The file gets written automatically if you call save_highscore();
and if it already exists it gets overwritten, so theres no need to delete the file before writing a new highscore over it.

I defined the file name in my example with:
#define HIGH_SCORE_SAVE_FILE "hs.score"

EDIT: thats not very secure... but with an easy encryption it should be secure enough
EDIT#2: if you need some help with en- and decrypting the highscore let me know