Sorry to hear that you’ve managed to damage your iPad screen with your Apple Pencil. Whilst the screens are remarkably robust, it only takes a particle of grit to be embedded in (or caught beneath) the tip to cause permanent damage.
I very much doubt that you will have any recourse to waranty for the damage. If you puchased AppleCare+ for your iPad you should be able to make a claim for screen damage - subject to an excess/duductable fee. Alternatively, perhaps your home insurance may provide insurance cover.
The best form of defence is always prevention. Personally, when using an Apple Pencil (or other stylus), I always recommend installation of a good quality screen protector - as this is a sacrificial layer that can be easily replaced if damage should occur. Unlike the tip of your finger, where you can feel so something abrasive, when using the Pencil it is very difficult to detect something on the screen that might cause damage before it’s too late.
If you suspect that your Pencil caused the damage, you would be well advised to change the tip. An abrasive particle can embed itself in the soft tip - and continue to cause screen damage with futher use.
Hope this provides you with some useful advice.