it looks like the picture is complex and nuanced
the full study is here
https://journals.sagepub.com/doi/10.1177/15648265070284s407 ( click PDF)
it shows a rather mixed picture - with conflicting findings in many trials
it does seem that the degree of parasitology remained higher for longer in the blood of those who were given folate and iron - vs those who were not - but, significantly, clinical outcomes were no different in the end
it seems likely therefore that while there is an effect on the parasite - overall its not a very large one in terms of patient outcomes
the effect was also present in one species malaria (P. vivax) but not in the other(P. falciparum)
therefore if you are not treating malaria at all - but Babesia or other species - one has to be cautious in applying the above findings - as although they are related, these organisms are all considerably different to malaria - much more different to malaria than different species of malaria are to each other - and therefore its somewhat unlikely that the conclusions will hold true for Babesia.
since clinical outcomes were largely the same - i am not sure its worth worrying about