The Song:

In order for it to feel more authentic, Beck filled out his Song Reader book with fragments of songs and melodies, as well as fictional album collections and song titles. "Grin" can be found on the collection of manly hymns, Hymns For Him.

Many of the titles throughout Song Reader are references to older sheet music/songs. I was unable to find one called "Grin" but the relative generic nature of the word makes it seem quite likely to me that it does exist. Beck probably saw reference of it and included it.