The court is not part of the Executive Branch of government. A democratic government, like the United States, is composed of three different branches that perform their specific tasks to aid the government and its people. These three branches are the: Executive, Legislative, and Judiciary.
The court belongs to the Judiciary branch of the government upholding justice and making decisions for the land based on existing laws. The Judiciary is a separate power in government that can mitigate its powers in both the Legislative and Executive branches of the government.