I fully understand your concerns and you'll see when prompted to enter the bank account details that the secure socket layer is established (https shown in the URL) so the characters are encrypted as you type and like all financial institutions even if TransferWise were to store what you type no one would be able to decipher what is stored. Even your own bank cannot tell you what your password is, they don't know, which is why if you forget your password the best they can do is to create a new one.
SSL (https) only encrypts the connection. The data is decrypted at the other end. At that point the server code will perform a one-way hash of the password, perhaps with a random salt, and store it. Because this is one-way it can't be reversed to get the password. That is why your bank says they don't know your password.
However, what hackers do is get the entire database with these hashes. Then they can take their sweet time performing one-way hashes on all kinds of passwords until they get a match. Then they know your password.
For example suppose your password is "dog" and after the one way hash it becomes 6215321FAD1. That is put into the database.
Now I hack in and get a hold of 6215321FAD1 along with your username.
I hash "cat" and get something different - no match.
I hash "pig" and get something different - no match.
I hash "dog" and I get a match. Ah ha! Now I know your password. Perhaps you have used this on other sites as well with the same username?
Actually it's worse than that. The same hash value can be obtained from different passwords. That's because there are less possible unique hash values than there are possible unique passwords. So perhaps I hash "mouse" and I get a match. Now I can use that as your password! This weakness depends on exactly how good the hash method is that is being used.
The hackers have fast computers, armed with dictionaries and common patterns, so they can check very quickly - millions of possibilities a second.
So that is how hackers can find your password. Always use something long and random without words in it.
However there is always the weak point - the moment when you password is received at the other end and before it is stored or compared with the database. I trust my bank and their server code. But do I trust some company that is relatively unknown to me? I decided not.
![Grin ;D](https://www.talk.uk-yankee.com/Smileys/classic/grin.gif)
Next time I need to make a transfer I will use my approach of temporarily changing the bank password so Transferwise only gets that one, then change it back. I would have preferred the "two small deposits" approach that XE and paypal use.