In a newly surfaced video from CPAC, Ms Greene grouped Guam with the United States' major foreign competitors as she called for the hard-earned tax dollars of Americans to be spent at home in America, not "wherever".
The Guam governor's office said it would be "more than happy" to send Ms Greene a copy of "Destiny's Landfall: A History of Guam".
The offer was made in The Guam Daily Post after Ms Greene's speech from the Conservative Political Action Conference in which she urged the US to stop sending aid overseas. While the speech was reportedly given on 27 February, video began doing the rounds on YouTube this week.
"I'm a regular, normal person. And I wanted to take my regular – normal person, normal, everyday American values, which is: we love our country. We believe our hard-earned tax dollars should just go for America – not for what, China, Russia, the Middle East, Guam – whatever, wherever," Ms Greene said.
"If we want to build roads, if we want to put money into schools, if we want to build border walls, we want it right here at home. This is easy to me; it's easy to us, but it's not easy to Washington."
With roughly 170,000 federal tax-paying residents, Guam has been a part of the United States since 1899 and people born in the territory have been citizens since 1950.
Guam's House of Representatives delegate, Michael San Nicolas, told the Post he would engage in some cookie diplomacy to welcome his freshman colleague.
"Congresswoman Greene is a new member, and we will be paying a visit to her and delivering delicious Chamorro Chip Cookies as part of our ongoing outreach to new members to introduce them to our wonderful island of Guam," he said.
The former chairman of Guam's Republican Party, Phil Flores, told the Post he tried to call Ms Green's to no avail, and instead left a message with an office assistant.
"I said Guam is a part of America. We have been for 122 years," he told the outlet.
"You see it every once in a while, 'Where's Guam?' And obviously, we don't expect to be as well known in the mainland as perhaps California or New York, but more people should know about this wonderful part of America."
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