My phone’s home page for the Internet is a Google search page. When I put http://m.nutmegstatefcu.org in the search field, Mobile Banking doesn’t show up.

Do not put the URL for Mobile Banking in a search engine’s search field. Instead, use the browser’s Menu button and select the item where you can enter a URL directly, e.g., “Go to” or “Go to URL”, or click on the URL locator bar at the top of the browser and enter the URL directly.