This reconstruction era policy gave voting rights only to people whose grandfathers had been legally allowed to vote

Grandfather Clause is the correct answer.

The Grandfather Clause was a way found to deny suffrage to the black population. It was a Reconstruction Era policy that allowed only people, whose grandfathers were voters, to vote. Thus, freedmen were left out from voting. In 1915, the U. S Supreme Court found this clause to be unconstitutional since it violated equal rights that had already been guaranteed by the 15th Amendment. However, it wasn't until 1965 that Congress was able to end this discriminatory practice.