Removing a field group form a page does not remove the data in those fields from the database.
There is no way for me to know what exactly you need to do. It could be as simple as deleting the content of those fields which would mean having the field on the page and deleting the content. Or could be that you actually need to alter the code in the template. All of this depends on the fields and the code used to show them.
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users