Liz Danvers (Jodie Foster) is listening to a white noise track while working. White noise can reduce fatigue, improve overall concentration, and help memory when used at night. It also creates a consistent background sound that allows for better attentiveness.
At around 32:00 when Navarro is trying to get information about the whereabouts of Oliver Tagaq from Qavvik, he wants to use "quid pro quo" with her to learn more about her life. Quid pro quo was a major theme of The Silence of the Lambs as Clarice Starling (Jodie Foster) used it to get information from Dr. Hannibal Lecter. Jodie Foster plays Liz Danvers in Season 4 of True Detective.