Our works, however noble and mighty, are simply not enough and perfect enough to make the difference. Unless our righteousness is as the righteousness of Christ then our righteousness is not good enough. That excludes all of us. But by faith we can receive the righteousness of Christ. By faith in the finished work of Christ on the Cross, we can receive God's grace.
Grace is unmerited favor.
It is forgiveness for sin when we deserve condemnation. And this is exactly what Jesus offers us if we will surrender our lives to Him. This woman can teach us a great deal about how to approach God. We must approach Him in faith - a faith that acts. We must be persistent, yet humble.