How does preventing grace lighten the effects of original sin?
It prevents the full consequences of our alienation from God and awakens conscience, giving an initial sense of God and the first inclinations toward life in its fullest sense.
Catechism for the Global Methodist Church, question 51
45Then he opened their minds to understand the Scriptures.
37All that the Father gives me will come to me, and the one who comes to me I will never cast out.
32And I, when I am lifted up from the earth, will draw all to myself.
14A woman named Lydia, a dealer in purple from the city of Thyatira, who worshiped God, was listening; the Lord opened her heart to pay attention to what was spoken by Paul.
7Because the purpose of the flesh is hostility toward God, for it does not submit to the law of God, nor indeed is it able. 8Those who are in the flesh cannot please God.
14The natural person does not receive the things of the Spirit of God, for they are foolishness to him, and he is not able to understand them because they are spiritually discerned.
Question 51 takes the definition of preventing grace from question 50 and asks what it actually does. The answer is lifted almost word for word from ¶102.3 of the Book of Doctrines and Discipline, which says that preventing grace "prevents the full consequences of humanity's alienation from God and awakens conscience, instills a basic knowledge of the moral law, gives an initial sense of God, and restores a measure of liberty to receive the further graces of God, all of this issuing in the first inclinations toward life." The catechism compresses that list into three effects: the worst is held back, conscience is awakened, and a first sense of God and inclination toward life is given.
The references first describe the condition being addressed. Paul says "the purpose of the flesh is hostility toward God, for it does not submit to the law of God, nor indeed is it able" (Romans 8:7), and "the natural person does not receive the things of the Spirit of God, for they are foolishness to him" (1 Corinthians 2:14). Article VII of the Confession of Faith says the same: fallen humanity, apart from grace, "is destitute of holiness and inclined to evil." Left alone, the human will does not want God. That is what "the full consequences" of alienation would look like.
The remaining references show God interrupting that condition from the outside. Luke reports that the risen Jesus "opened their minds to understand the Scriptures" (Luke 24:45). At Philippi, Lydia was listening, and "the Lord opened her heart to pay attention to what was spoken by Paul" (Acts 16:14). Jesus promises that when he is lifted up he "will draw all to myself" (John 12:32), and that "the one who comes to me I will never cast out" (John 6:37). The drawing is his work, and the coming is the response that drawing makes possible. That is what the catechism means by an awakened conscience and "the first inclinations toward life in its fullest sense."
For a Methodist this explains why the church expects to find conscience, moral seriousness, and a hunger for God in people who have not yet believed, and why it treats those things as signs of God's activity. If God opened Lydia's heart while Paul was still talking, he may open another heart during any sermon, and the preacher's task is to speak the word that grace uses (Acts 16:14).