It's that particular registration board's precinct number. Here's a passage from board registration instructions (the section for registrars on how to fill out the cards) in 1917's "Registration Regulations Prescribed by the President Under Authority of the Act of Congress Approved May 18, 1917" (page 20, step 52):
"52. Authentication. Now turn the card over to the registrar's report. If you think any of the person's answers are incorrect or false, note which and in what respect on the blank spaces left after your certificate and then, whether you make such entries or not, sign the card. [Then in italics]: Last of all, number the card in the upper right-hand corner in one series for your precinct. Note--If desired, cards and certificates may be numbered before registration...."
I'm not positive what each of the three numbers stands for but I think the first number indicates the state, the second number the district, and the third number the local precinct. All the cards I have from New York state for instance start with the number 31; from Pennsylvania, 37. All the cards for draftees from my small home county bear exactly the same three numbers; cards from other counties or cities still have the same first number (the state) but the second and third numbers vary. Any two cards from the same place always bear the same numbers.
The letter at the end, I think, relates to the draft registration period. All the cards I see for people who registered in the first call, on June 5 1917, bear the letter "A," and in the second call, on June 5, 1918, the letter "B." I don't have examples of cards from the third call, later in 1918, but my guess would be they bear the letter "C."
Unfortunately, none of this tells you anything more about your grandfather, but I hope my answer (admittedly confusing, probably clear as mud!) helps somehow.