ToS are not enforceable if you don't use an official product feed from Amazon in this case. As shown by thousands of companies providing exactly this service for competitor analysis.
i think they mean the ToS for amazon's affiliate link service, which prohibits earning a commission if your site has price history (a few large and old sites have exceptions)
Ah, from the wording ("pull") I assumed you were using the API. You use your own user-agent to access the site(s) and collect prices then? Do you have any trouble getting blocked doing that? Is it some headless chrome controlled programatically?
I have another site that made some qualified sales, so I can use the APIs.
I also played a bit with scraping, and you can do that quite easily, but if you want to do it at some scale, you need lots of proxies, and quite soon it gets slow and overkill