OP's linked paper has "the iron-reduction patients had 300ml of blood removed at the start of the trial and between 250 and 500ml removed four weeks later."

A blood donation removes 500 ml, so about a year of menstruation all at once. You can donate every two months, besides.

So, yes, if there is an effect then we might expect the magnitude of the effect to differ. Or else we'd expect a paper cut to also have the same effect.

Sex biological difference could matter as well.