ANSWER:
Jinns do eavesdrop but what they hear is very negligible.
Al-Bukhaari (6213) and Muslim (2228) narrated that ‘Aa’ishah (may Allaah be pleased with her) said: Some people asked the Messenger of Allaah (peace and blessings of Allaah be upon him) about soothsayers. The Messenger of Allaah (peace and blessings of Allaah be upon him) said to them: “They are nothing.” They said: O Messenger of Allaah, sometimes they tell us something that turns out to be true. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “That is a word from the jinn that the jinni snatches, and he cackles it into the ear of his familiar as a hen cackles, but they mix more than a hundred lies with it.”