The idea of righteousness changes from the Old to New Testament. In Romans Paul explains a little more about the gospel and the new righteousness, or new path to righteousness, i.e. faith, as opposed to keeping the law perfectly.
I think we still struggle with that transformation in our lives a Christians. We are concerned with right and wrong and want to do the right thing, but certainly know the frustrations of not being able or sometimes even willing to do this as Paul also relates in Romans 7.
I want, again, to reiterated that we are considered righteous in God’s eyes by virtue of what Jesus has done. Therefore I would want people to embrace the gift of righteousness, relax just a bit, and do what we do out of love and gratitude for God. There is nothing we can do to become more righteous. There is nothing we can do to have the abundant life of God flow through us more freely, being a blessing to us and those around us.
Scripture Reference: Romans 3