What was the term used by Southerners for a return to Democratic, white
rule?

Redemption      

Explanation:

The Southerners use the term redemption (redeemers) for the return of the white rule in the South after the Civil War in America. They were the Southern democrat's wing which was part of the democratic party in the South. Redeemers tried to recover their political power to control the South. They were also against the carpetbaggers, scalawags, and some of the Republican people who control the Reconstruction era which began in 1867-68.      

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