[T]he beginning of the said Justification is to be derived from the prevenient grace of God…
Once again we see that justification is by grace ("Prevenient" == "preceding in time or order; antecedent," for those who don't know and might not take the time to look it up themselves).
…through Jesus Christ…
If justification is through Jesus Christ, it is not something we achieve on our own.
…whereby, without any merits existing on their parts, they are called;… [emphasis added]
Justification is by the grace of God, through Christ, without any merits on our part: therefore we cannot deserve to be justified; therefore we cannot earn it; therefore it is not a human work; and so those who say we believe in "works-based" salvation are horribly misinformed.
Now we come to a portion of this chapter that perhaps some wrest from its context, so as to make it say what they wish.
…that so they, who by sins were alienated from God, may be disposed through His quickening and assisting grace, to convert themselves to their own justification, by freely assenting to and co-operating with that said grace: in such sort that, while God touches the heart of man by the illumination of the Holy Ghost, neither is man himself utterly without doing anything while he receives that inspiration, forasmuch as he is also able to reject it; yet is he not able, by his own free will, without the grace of God, to move himself unto justice in His sight.
Now some might jump on the phrase "to convert themselves to their own justification," and say "Aha!" But they who do so are misunderstanding things if they think that this means we are able to save ourselves.
What is being said here is really nothing more than what we saw St. Thomas teaching about the role of free will in our salvation, and as we have seen St. Augustine say: namely, that our salvation is not accomplished against our will. We must certainly consent, but that is hardly the same as saying that we save ourselves. We see this in what follows: "[man] is not able, by his own free will, without the grace of God, to move himself unto justice."
An analogy here is that the drowning man cannot save himself; the life preserver must be thrown to him. He is free to reject that salvation: he may choose not to grab hold. But the fact that he does grab hold would hardly be cause for anyone to say that he saved himself. The claim would be lunacy.
(This is not a perfect analogy, of course, because in the case of our justification we are not able to reach out for salvation apart from God's grace.)
When I was a Calvinist, I once saw a (Calvinist-authored) comic which tried to turn this analogy on its head, claiming that we don't even grab hold of the life preserver, because "dead men don't grab the life line" (or words to that effect; I'm paraphrasing from memory): the claim that is made is that we are "dead" in such a sense that we cannot even exercise sufficient free will so as to grab hold of Christ.
There are a variety of problems with this claim. First, as long as we draw breath on this earth, we're not dead in any literal sense. Not even Adam died in a literal sense when he ate the fruit: His body remained alive; his soul remained alive (this is not to say that there was no sense in which he did die that day; of course there was). So to try to make a claim that we're "dead" (which can only be taken in some literal way, if the criticism is to hold), and therefore cannot assent to our salvation, is just wrong.
Secondly, it flies in the face of the whole of Scripture, where we are told over and over that we must choose, and that we must repent, and that we must save ourselves. Does it make a lick of sense to deny, then, that an act of our free will (being enabled by God's grace) is necessary for salvation? I don't think so. The nonsensical thing is to subject this constant testimony of God's Word to nullification by way of so-called "letting Scripture interpret Scripture." Now of course it's true that some parts of the Bible clarify others, but there is absolutely nothing unclear about the fact that the Bible calls for us to make a choice for God, to repent (which is an act of the will), and so forth. None of this means that we save ourselves, as in the illustration previously given. The fellow who is trapped in the burning building doesn't pat himself on the back that he reached out to the fireman on the ladder: he knows exactly how he was saved, and only a deluded narcissist would think he deserved credit for it.