Since God has deliberately chosen not to predestine them to Heaven, has He not then deliberately damned them?
The Catholic tradition is a lot more nuanced than a simple answer can explain, and there are a number of different possible answers. Being predestined to Heaven doesn’t mean that God saves some, and does nothing for others, but rather that those who are carried to Heaven are carried by Grace, by the Will of God, and those who sin are abandoned by Grace due to their sins, due to their abandoning of Grace.
Here’s my thought on the matter, based on the Councils and on Aquinas.
That people are certainly known to be Damned doesn’t mean that God doesn’t give the opportunity for salvation to the Damned, it just means that being omniscient He knows their destiny before hand, and Wills to allow them to ultimately fall away according to their free will (the free will which God provided them). The predestined, on the other hand, can only be carried to Heaven by Grace, not by their own natural merits, so God supplies Grace for the predestined in order that they may be in Heaven with Him (obviously they work with this Grace too, but that is another issue); God knows they will be in Heaven by His omniscient foreknowledge, and provides the means, namely Grace.
This is why, for example, the Catholic Church can say definatively that Baptism imparts real Grace, but that those who have been Baptised can go to Hell. God gives the same Grace to both types of Baptised (the ultimately Saved and the ultimately Damned), but those who fall away from Grace gain nothing from it in the end. So the negative reprobation of Hell is less that God doesn’t do something for them (except in the sense that He doesn’t bring them to Heaven), and more that He permits them to be lost by their sins.
So let’s imagine that I have a bowl of different colored marbles, and I somehow know that only blue and red ones will remain in my hand, though there are many other colors (let’s say those other colors also happen to bounce around, like mexican jumping beans), and I wish to carry the blue and red marbles away. I reach into the bowl and lift them all up, and as I raise my hand every marble that isn’t blue or red falls away one by one, and I now have all of the blue and red marbles just as I had planned.
I knew beforehand that only blue and reds would come with me, and I put my hands in to grab those blue and red marbles (omniscience and predestination), but I didn’t forsake the other marbles, rather they fell away from me on their own (negative reprobation). I allowed them to fall away, but it’s a different situation than if I simply went through the bowl and only picked out the red and blue ones, passing over the other colors. The red and blue are carried up by predestination, and the others are lost by reprobation, but the red and blue can be said to be lifted up only because I lifted them, not because they could compel my hands (and not because they could come up by any means other than my hands), and the others can be said to be lost only because they fell away, though it’s true that I could have theoretically forced them, against their inclination, to remain in my hands (and God could destroy the free will of those who are Damned, too, but that would be to destroy them in the process).
So it’s an incredibly subtle and nuanced issue, but hopefully this helps clear things up.
Peace and God bless!