Your question: "What influences God in the granting of salvation?" asks that I speak for God, which I cannot rightly do...but The Urantia Book does give us clues on this subject
When our Master revealed to us the true nature and character of God, he demonstrated by his very life that God goes out in search of the wrongdoer, as the true shepherd leaves the flock to go out in search of the lost sheep. Since our Heavenly Father is changeless and perfect, his divine purpose has always been to constantly minister mercy and to show unwavering goodness to every being. It is literally true: He would "have all men be saved by coming into the knowledge of the truth." He is "not willing that any should perish."
God desires that all be in communion with him. We are all beloved sons and daughters of God. It is only the continued rejection of the Father's constant proffer of divine mercy that distances the wrongdoer from experiencing the unqualified love of God. The Father never wavers from his boundless mercy. Man need not be saved from God's wrath, but he most certainly needs to be saved from himself, from his own base and selfish tendencies.
"God is inherently kind, naturally compassionate, and everlastingly merciful. And never is it necessary that any influence be brought to bear upon the Father to call forth his loving-kindness. The creature's need is wholly sufficient to insure the full flow of the Father's tender mercies and his saving grace. Since God knows all about his children, it is easy for him to forgive." The Urantia Book 2:4.2)
Finally, I would have to say that since God knows each of us better than we even know ourselves, we can rest assured that God can read our inner motivations and desires fully. If your life is pointed God-ward, he surely takes note of that, in spite of our tendencies to falter and err on the way.
Thanks so much for your question—I hope this reply has been helpful.