I have seen one time in some forums and typically in HP Forum archive 13 in May 2003 some questions about how to recalibrate the HP-01 clock and some other questions about the quartz frequency, etc...
As I have got one of those watch I was trying to find answers.
I will say that answers are in HP journal December 1977
According to schematic page 4:
Quartz is 38.4 kHz
C3 adjustable capacitor position can be seen in page 7 figure 7.3
Physical position can be deducted from photographs
Looking at the back inside of the watch, find the hole (1.8 mm diameter) where it can be adjusted.
See attached photograph.
A small isolated square ended tool has to be used to perform the adjustment. From an old small screwdriver I build a such tool and it is approximately a square of 0.65 mm. I am not sure about isolation but I have done it just in case.
I hope this information will be useful to others.