40 mW divided by 3.3 V implies a current of about 13 mA. So choose any size rated for at least twice this amount for margin with low resistance and the cheapest price.
When an inductor exceeds it rated current, it will lose its inductance, like a spring bottoming out so it acts as a noise filter or low pass filter if there is any noise on the 3.3 V supply. Low supply noise is important for the liquid paper display.
It is not clear to me why or where an iron core inductor was specified but these tend to have higher permeability and thus less wire and lower resistance. The reason I mention this is when switching the inductor the current rise is due to the ratio of L/R=T time constant. The max current is Vcc/ESR of the total resistance but the current must be only pulsed for a low duty cycle such that the average current is only . The FET is < 0.3 Ohms the series source is 3 Ohms so I suspect the inductor needs to be similar to the R values of iron core parts with 68uH which is < 0.5 Ohms but it does not have to be iron core, per se.
They should have specified part numbers in the BOM.
Here is my Rev A choice https://www.digikey.com/products/en/inductors-coils-chokes/fixed-inductors/71
I have changed my selection based on <=0.5 Ohm rather than >> 13mA so you will find it rated for much higher currents, even tho it will be limited by the total equivalent series resistance (ESR) of R(L1+Q1+R2)= 0.5+0.3+3 = 3.8 Ohms thus current ramp is 68uH/3.8 Ohms = 17 us. (??) and if pulsed for this duration the ramp current rises towards 3.3V/3.8 Ohms = 870 mA To use less than 13 mA average ( assuming that is correct) the pulse duty cycle must be 13/870*100=1.5% hmm