No, that is clearly not about law of Moses. This is the passage in context:
For we ourselves also were some time unwise, incredulous, erring, slaves to divers desires and pleasures, living in malice and envy, hateful, and hating one another. But when the goodness and kindness of God our Saviour appeared: Not by the works of justice, which we have done, but according to his mercy, he saved us, by the laver of regeneration, and renovation of the Holy Ghost; Whom he hath poured forth upon us abundantly, through Jesus Christ our Saviour: That, being justified by his grace, we may be heirs, according to hope of life everlasting. It is a faithful saying: and these things I will have thee affirm constantly: that they, who believe in God, may be careful to excel in good works. These things are good and profitable unto men. (Titus 3:3-8)
"Righteousness" instead of "justice" is fine, -- it is the same Greek word. The passage speaks of good works in relation to Divine Mercy, and surely mercy is unearned and not of works; mercy is a component of grace, by which alone we are saved. Appropriately, the passage ends with an exhortation to good works. It is very similar to the beginning verses of Ephesians 2, and like Ephesians 2 speaks of salvation by grace (or mercy) alone, to which men respond with faith and with good works.
Again, nobody has denied believers should be careful to excel in good works. We do so out of gratitude to God for His grace. But these works are "good and profitable unto men", they honor God and help our fellow man. God rewards our righteous living in this life and into eternity. BUT...it doesn't say they are for our salvation. God HAS saved us by His grace and mercy and we receive His gift of eternal life through faith - not by our works, as if we must add to Christ's work or do our work to keep the gift He freely gave us.
You have been arguing this topic for as long as I can remember and there are times that I think you're right on the edge of finally getting it but then you step back and go downhill to the accursed Gospel of works righteousness.
When we face the Lord at our judgment, we won't be carrying a bag with all our good deeds to lay on a scale hoping to outweigh all the bad deeds we did in this life to determine if we go to heaven or not. No, we will approach Him either clothed in the righteousness of Christ, His white linen garment of salvation washed in HIS blood draped across our shoulders or our own filthy rags of righteousness. This is because it is ONLY by the shedding of blood that we have our atonement for our sins. All the good deeds, law keeping, works of love or kindness or corporal works of mercy - no matter how many we did - can never take away our sins. Only Christ, in our place, can do that. We won't be saved by any righteous deeds we have done, but because of HIS mercy and grace. Eternal life is His gift to us and we receive this gift by faith, trusting in HIM to save us. We respond to His offer by our faith and the changed life that results from being a new creation, having a new spirit nature with the indwelling Holy Spirit within us as the earnest of our inheritance, we now have the desire to please God by how we walk in newness of life. Our works don't save us, Jesus saves us. Our works don't keep us saved, Jesus saves us to the uttermost.
that they, who believe in God, may be careful to excel in good works. These things are good and profitable unto men.Titus 3:8
Oh really?
Righteousness - צְדָקָה - tsedaqah - Strong's #6666
judgment - κρίσιν - krisin - Strong's #2920
You perhaps should correct the Greek scholars on that. They would certainly be interested in your "explanation" I would think.