"How much more shall the blood of Christ... purge your conscience from dead works to serve the living God?" (Hebrews 9:14)
What are these dead works that are in the conscience of man? They are the remnants of un-enlightenment, remnants of misunderstanding. However, the cleansing from dead deeds DOES NOT mean that the person continues to sin! He lives a life in faith, a renewed life in Jesus Christ in him.
Let us use an example here. A man is drowning in a swamp, the dirty water is pulling him deeper and deeper in, and soon he will drown! Someone extends a hand and pulls him out, unto the dry ground and saves him. Does this person have a reason and a right to thank his savior? Of course he does, he almost drowned, died, but now is saved even though the dirty swamp still soaks his clothes and is dripping from him! This example is used to show a person who has come to faith.