Pro-Israel news outlet HonestReporting publicized Amanpour's initial comment on May 11, after it had gone under the radar for a month already.
The Foreign Ministry confirmed that it is working on a complaint, after a source saw a draft of the letter.
IDF spokesman Daniel Hagari was interviewed on CNN and mentioned, among other things, the anniversary of the death of the Al Jazeera journalist in Jenin.
The prime minister stressed that he opposes allowing a simple majority to override High Court of Justice decisions.
The CNN journalist in question is Tamara Qiblawi, a Georgetown-educated Lebanon native who has worked for CNN since 2015.
Former Mossad head Efraim Halevy alleged that Netanyahu deliberately hid his judicial reform plans from the public in order to win the election.
The box primarily contained old presidential schedules with a few classified records among them, according to CNN.