We Christians can read this as reassuring.
We should be grateful but not triumphalistic.
Further, we should be careful not to misinterpret the phrase, "dead works."
According to Allen & Williamson's Preaching the Letters without Dismissing the Law
The "dead works" should not be confused with the mitzvoth of torah. "Dead works" are not "deeds of loving kindness"; they are sins that pollute the conscience.