The excerpt has the characteristics of a 'Neoclassical' poem, including its usage of 'heroic couplets' and its 'elevated' style of language.
The correct answer is their. Because his or her wouldn't make sense because it says they, his also wouldn't make sense for that reason, and the other form of there means for example, "over there"
Means getting rid of something all the way with no other strings leading to it.