‘Then he says, “And their sins and their iniquities will I remember no more.” '
And added to this will be the complete removal of their sinfulness. All their sins and iniquities, their outward failures (‘sins') and their inward sinfulness (‘iniquities'), will be remembered no more. They will be deliberately obliterated from God's memory. ‘Remembered no more' is, of course, hyperbole to express the completeness of God's forgiveness. Nothing that they have done or failed to do will be counted against them any longer.
So His covenant offers a new freedom to obey God, and a dealing with the spiritual death (Ephesians 2:1; Ephesians 2:5), bondage (Mark 10:45; 1 Corinthians 6:20; John 8:34-36; Romans 6:6; Romans 6:14; Romans 6:17-18), indebtedness (Colossians 2:14) and alienation (Colossians 1:21; Ephesians 4:18) caused by sin