The correct answer provided in the question is option 2: "An integral part of the United Nations" is not correct.

Option 1: "A group of developed countries" is a correct statement. The G-20 is a group that consists of both developed and developing countries. It includes some of the world`s largest economies.

Option 2: "An integral part of the United Nations" is incorrect. The G-20 is not a formal part of the United Nations and operates independently. It was established in 1999 as a platform for cooperation and discussion on international economic issues.

Option 3: "Outside the World Bank and IMF" is a correct statement. The G-20 is independent of organizations like the World Bank and IMF. However, it collaborates with these institutions to address global economic challenges.

Option 4: "An offshoot of G-7" is incorrect. The G-20 was formed in response to the shortcomings of the G-7, which consists of seven major advanced economies. The G-20 includes a broader range of countries and is more representative of the global economy.

In summary, the correct answer is option 2 and the other options provide accurate information about the G-20.