UK banks don't accept any liability if you give your online banking credentials to a third party. If some fraud was to come about as a result of someone using Teller then they would be out of pocket or has Teller got agreements with the compatible banks to overcome this situation (either by Teller reimbursing the customer or the bank)?
I'm personally waiting for the PSD II law to be deployed (see https://blog.teller.io/2016/04/26/tauth.html) in order to have clear-cut protections & boundaries, before leveraging Bankin or similar (Teller) as a SaaS product builder.