Methods for learning with noisy labels
First, I wouldn't use the word "noisy" here because if you know which instances are "wrong" then these are not noise, they are negative examples. In my opinion "noisy" is when positive and negative cases are mixed together in a way that makes it difficult (or impossible) to distinguish between them. I think this matters because you're more likely to find similar use cases and relevant methods using this terminology.

I don't have a precise method to suggest but I would check the state of the art in machine translation: it's also a sequence-to-sequence task in which there are potential positive/negative cases. In particular there has been some work done in MT quality estimation, where the goal is to predict the quality of a translation for a sentence. This might be related because it's about labeling or quantifying how good a translation is, and I would assume that there are works which re-use labelled/scored translations (including potentially wrong ones) in order to obtain a better model. Unfortunately I don't have any pointers since I haven't followed the field recently.