Because women and men have similar success rates for these grants, and the amounts awarded are usually the amounts requested, the authors think the discrepancy is because 'women are systematically less ambitious in the amounts of funding requested in their grant applications.'
They recommend that mentors 'should ensure that women are as ambitious as men in their outlook, and in their grant proposals'. But they don't consider the alternative explanation, that women who ask for as much as men do are seen as greedy and undeserving, while women with modest ambitions are rewarded. This might be checked by comparing the the requested amount with the probability of being funded, for men and for women.
Their second recommendation, that 'men should be encouraged to be economical when costing such applications', is of course absurd.