Ask HN: App using AmazonCognito to auth but it doesn't tell you in terms. Is ok?

Sorry if the title isn't OK - it had a limit. I am using a website where I had to register providing my real name, first name, last name, email address, etc. Checking the Network tab on Dev tools, I'm seeing the authentication is against Amazon Cognito. But I am checking the Terms of Service, Privacy Policty, etc., and they don't mention Amazon anywhere, so they are sharing my data with Amazon but I never accepted it. Is that right? I am not planning in any legal auction because this website is a monster, but I'd like to tell them via Twitter they should add a legal notice about it. I just wanted to be sure before being pedantic on a social network :-) Thanks!