In theory, international civil servants at the United Nations are prohibited from continuing to draw salaries from their own governments; in practice, however, some governments merely substitute living allowances for their employee's paychecks, assigned by them to the United Nations.
Sometimes its nice to solve a questions using the 2/3 split especially when the split is screaming at your face!
the split is between FOR vs IN--- probably indicates an idiom error!the correct idiom is "substitute X for Y".. therefore we can eliminate options D and E!
(D)
in place of their employee's paychecks,
for those of them assigned- this sentence also has a meaning error: we are not substituting paychecks with other paychecks-- and those is ambiguous it can refer to employees or paychecks!
(E)
in place of the paychecks of their employees
to have been assigned by them- usually to-verbs indicate an intention and there is not intention to assign to the United Nations its more like a fact!!- meaning error
(A) for their employee's paychecks,
assigned by them--- okay so verb-ed modifiers usually tend to modify the noun before them so what this sentence says is that paychecks were assigned by someone to the united nations--- ambiguity and illogical meaning!
(B) for the paychecks of their employees who have been assigned- "who have been assigned" relative pronoun modifier modifying employees and since there is no ambiguity in the meaning- we have a winner!(C) for the paychecks of their employees,
"having been assigned"--- okay so "verb-ing phrases either modify the action in the previous clause when separated by a comma(usually to indicate a cause and effect relation) and when not separated by a comma usually act as adjectives that modify the noun before them or after depending of where the verb-in word/phrase is present!--- so this option primarily illogically indicates that the substitution happened because of being assigned to the UN- illogical--- and we do not know what is assigned to the UN?