Christ told the people this to completely unnerve them. Their understanding of righteousness was wrong. He wanted them to understand that there was a new definition for righteousness and they had to let go the old definition.
The new righteousness is the righteousness of faith by which the righteousness of the Lord is imputed to believers in Jesus Christ.
The KingdomOfHeaven is the HolySpirit who issues from the SpiritRealm into the PhysicalRealm.