I think it's "to" as the indexical this/that as in To je Žofie. In this case "That must have been an interesting woman." But in English it is more natural to use a personal pronoun here.
In an earlier question's discussion I've seen "být" used in the present tense, where as here it appears to be used in the past tense. Is this the case here because of "musela" being past tense? Thank you in advance for any clarification.
"být" on its own is an infinitive ("to be"). Czech (like English) has only one infinitive, it does not distinguish infinitive tenses.
That it was her obligation?
Musela být zajímavou ženou. (or zajímavá žena, but I think the instrumental is better)
I guess I'm thinking of it as meaning the same thing as the Duolingo translation, which admittedly is better. I wasn't trying to make it out to be her obligation.