I don't know if anyone else is still scraping new images into the generators. I've heard somewhere that OpenAI stopped scraping around 2021 because they're worried about training on the output of their own models[1]. Adobe Firefly claims to have been trained on Adobe Stock images, but we don't know if Adobe has any particular cutoffs of their own[2].
If you want an image that screws up inference - i.e. one that GPT-4V or Stable Diffusion will choke on - you want an adversarial image. I don't know if you can adversarially train on a model you don't have weights for, though I've heard you can generalize adversarial training against multiple independent models to really screw shit up[3].
[0] All learning capability of text generators come from the fact that they have a context window; but that only provides a short term memory of 2048 tokens. They have no other memory capability.
[1] The scenario of what happens when you do this is fancifully called Habsburg AI. The model learns from it's own biases, reinforcing them into stronger biases, while forgetting everything else.
[2] It'd be particularly ironic if the only thing Nightshade harms is the one AI generator that tried to be even slightly ethical.
[3] At the extremes, these adversarial images fool humans. Though, the study that did this intentionally only showed the images for a small period of time, the idea being that short exposures are akin to a feed-forward neural network with no recurrent computation pathways. If you look at them longer, it's obvious that it's a picture of one thing edited to look like another.