Translation:The children needed the consent of the parents.
Being just an E3L speaker I cannot say whether “their parents” is more usual than “the parents” (when talking about the subject's parents).
Literally, “of their parents” would be translated as “de siaj gepatroj.” I imagine that it is possible to contrive scenarios where these two sentences have a different meaning, such as when a school class needs consent from all parents to go on an excursion. In such a case I would imagine that “the parents” is a suitable translation of “la gepatroj,” and “their parents” is a suitable translation of “siaj gepatroj.” Esperanto and English aren't that different here.
So I assume the question is not about a “better translation.” It's about a translation that reflects the speaker's intention.