An author's argument is the opinion or belief that he or she wants to persuade readers to believe.
What are the choices given here? Anyway, if the question is whether the sentence "The couple looked closely at the exterior of the house, they noticed; the paint was in disrepair." uses correct punctuation, I shall answer that it does not.
It could possibly be: The couple looked closely at the exterior of the house; They noticed the paint was in disrepair.
The thesis statement in the essay presents the aithor`s controlling idea.