This prayer seems to come from the Auxilium Christianōrum, which can either mean "Aid for Christians" or "Reinforcements/Backup Troops of Christians". They're an organization specifically dedicated to fighting and exorcizing demons. I've made only one correction to your text (adding a missing space) to bring it in line with the Auxilium's version (bottom right of the first page).
O Piisima Virgo Maria, quæ caput serpentis contrivisti,
O Most Blessed Virgin Maria, you who crushed the head of the serpent,
protege nos a vindicta mali.
protect us from the vengeance of the evil one.
Offerimus tibi dolores, bona, operaque ut ea purifices, sanctifices
We offer you our sorrows, o good one, and our works, so that you can purify them and make them holy
et largiaris Filio tuo sicut oblationem perfectam.
and that you might be imparted on us by your Son, just like the perfect sacrifice.
Hæc oblatio fit ne dæmonia qui afficere membra Auxilii Christianorum petunt
Let this offering be so that the demons which seek to affect the members of the Auxilium Christianōrum
cognoscant originem expulsionis et cæcitatis suae.
may not understand the source of their expulsion and their blindness.
Cæca eos ne nostra opera bona cognoscant.
Blind them so that they may not understand our good works.
Cæca eos ne cognoscant quos ulcantur.
Blind them so that they may not understand whom they would take vengeance on.
Cæca eos ut sententiam iustam operum suorum suscipiant.
Blind them so that they might receive a fair sentence for their actions.
Operi nos sanguine pretioso Filii tui
Conceal us [from them], with the blood of your precious Son
ut protectione quæ ab Passione Morteque ejus fluit fruamur.
so that we might enjoy the protection that flows forth from his Passion and his Death.
Hugh suggests that quos ulcantur should be quo sulcantur, which makes some sense. Sulcāre literally means "to make furrows in", from sulcus, "furrow". It usually refers to farmland getting plowed, or metaphorically, to some space being traversed. But when applied to a human (or, presumably, to a demon), it means "to whip" or "to strike with a lash" (i.e. making furrows on their skin). So the line would be:
Cæca eos ne cognoscant quo sulcantur.
blind them so they may not understand who is striking them with the lash.
But the "lashing" meaning of sulcāre is fairly obscure, and I don't think I've ever seen it in Christian usage: there are other, more obvious, words for lashing or beating someone (such as verberāre).
The other option, which I've taken, is be to postulate *ulci as a variant of ulcisci, "to take vengeance on", without its extra -sc- suffix. This lines up with the mention of vengeance up in line two (vindicta malī), and it seems simpler not to assume errors in an official publication. Basically, reading it as equivalent to ulciscantur "they would take vengeance on", with its direct object being quōs "whom (pl)". In other words, you're asking Maria to blind the demons so that they forget who they're supposed to be attacking.