Importunities noun \ˌim-pər-ˈtü-nə-tē, –ˈtyü-\
a: an importunate (troubesembly urgent/annoyance) request or demand
She arose at length and opened the door to her sister’s importunities.
The Story of An Hour paragraph 10
Importunities looks like the word important and although the of the words definition meant annoying urgency I thought it just meant her sisters urgency was important.