Here's what they say they do [1].

[1] https://support-my.plaid.com/hc/en-us/articles/4410324401047...

Relevant section for the "we do store your password" case:

    In other cases, when you link a financial institution to an app via Plaid, you provide your login credentials to us. We store those credentials and use them to collect the data to power the services you’ve chosen and, when requested, securely share it with the app you’re using and establish a secure connection that you control. We then help keep your data safe and private with best-in-class encryption protocols.

Sorry but this has zero meaning and I maintain: Red bloody flag. If there's any actual proof out there of them doing all this in a secure way, I'm happy to have my mind changed but this is just part of said marketing fluff.