The Reformed and many Lutheran theologians like Gerhard and Quenstedt agree with Luther and the Lutheran confessions on this issue insofar as it relates to human righteousness before God. Nevertheless, they disagree that the image of God is completely destroyed. This is not because they hold that there is some sort of remnant of original righteousness that could establish our relationship with God. Rather, it is because for them the image of God is also tied up in the knowledge of the law of God and the ability of human reason to exercise dominion in creation. This, again, does not mean that there is something of a point of contact between fallen human nature and God's grace. Rather, it is simply a recognition that humans possess an ability to engage in civil righteousness coram Mundo, and this is an expression of the divine image.
I personally think that these positions are in fact reconcilable if understood in terms of coram relationships. I think that accommodating both views is also necessary exegetically. Obviously in Genesis 1, the image of God and the original righteousness are tied up with humans serving as God's viceroys in creation. The Fall has not abrogated that role, just made it more difficult. Moreover, the Noahic covenant, when talking about murder teaches that murder is wrong because it defaces the image of God in humans. This presupposes that there is still a presence there, especially inter-human relationships.
Therefore, perhaps a good way of stating the answer would be that coram Deo, the image of God is utterly destroyed. This is what I think the Lutheran Confessions mean. Their point is not that humans have no ability to act morally regarding civil righteousness, but rather that God does not recognize his image in humans and therefore cannot count them as righteous. It is this image coram Deo that is renewed by faith and sanctification. Coram Mundo, humans can recognize the imago Dei in other humans through exercise of civil righteousness and the technical goodness that this involves. Nevertheless, such a remnant is not recognized coram Dei and in no way contributes to our relationship with God.