Phillips did not make screwdrivers. They took licensing fees from manufacturers and assigned them a license number for the right to make screwdrivers with their patented cross-recess tip. You will see it stamped on the shank or ferrule, usually in abbreviated form, followed by a hyphen and a number (e.g., LIC-4, etc). If it is indeed a Blue-Point screwdriver, it should be a LIC-1. I have a little running tally going in a sort of flea market cheat sheet/guide I publish for WWII collectors, since sometimes we run into unbranded screwdrivers, or screwdrivers with a worn marking, in which case (like yours!), the License # can help identify the mfgr.
LIC-1: Stanley, Blue-Point
LIC-2: IRWIN, Apex
LIC-3:
LIC-4:
LIC-5:
LIC-6: Vlchek
LIC-7: BHM
LIC-8: Bonney
We're not sure why some mfgrs shared a license number. One theory is cooperative fees. Another is one mfgr who owned the license made them for another (i.e., Stanley for Blue-Point).
As a point of interest, in 1937 Phillips had 4 licensees. By 1942, there were 19!