How to remove your images from the dataset
The creator is correct to tell you the dataset only contains URLs. This means you can still remove your images, and they will be removed even for those who have already downloaded the dataset, provided they haven't fetched the images yet. Since the creator claims the total size is 12 terabytes, it is unlikely that anyone but them has downloaded the full set, so there is still time to delete them before others do.
All you need to do is delete the images from Cara. If Cara does not retain deleted images, the URLs in the dataset will become useless. Because Cara uses a CDN, deletion may take some time to propagate, and while I have not verified whether Cara retains deleted images, the image should not be available for download afterward if they follow their own Terms of Service. I do not know if they offer a bulk deletion option, but closing your Cara account should also delete all your uploaded images, provided they do not retain them for their own use.