The exchange emerges in the latest, wider batch of documents released by the US justice department.
The emails were published by the US Department of Justice as part of a release running to three million pages.
The House of Lords is soon due to debate whether to introduce a legal ban on smartphones in schools.
More than one million people missed the deadline a year ago, according to HM Revenue and Customs.
The furry dolls have a signature spiky-toothed grin and became a viral purchase last summer.