It's a bit of a mess.
Some people argue that retraining is a necessity, and that the principle of data protection by design and by default requires a controller to have thought about this in advance, and factored it in. But it's not clear how many have done so.
Others argue that the right to erasure or right to object do not arise in the context here, or else that, if they did, it would be down to the presentation end to filter out the personal data.