Why did those who wanted to rewrite the Texas Constitution following following Reconstruction call themselves Redeemers?

They intend to rebuild their political power and enforce or redeem white supremacy. Hence, the name Redeemers.

Explanation:

The Redeemers were Southern faction of the Bourbon Democrats, the conservative, pro-business part in the Democratic Party, they are considered to be a political group in the Southern United States during the Reconstruction Era after the Civil War, around the 1870s to 1910.

Their purpose is to regain political power and enforce white supremacy, such that, their policy of Redemption was to remove the Radical Republicans, that includes coalition of freedmen, "carpetbaggers", and "scalawags".

Their leaders were rich former planters, businessmen, and professionals, and they dominated Southern politics in most areas.