The author fails his own test (Score 1)

The best response is to cancel the transaction. The question about using an extra secure connection is unexpected. Either software would be set up for the special connection when you first set up an account, or some big announcement would be made on the website - it's highly unlikely a site would choose to surprise users in such a way. That fact that the author would think any choice he presented is valid shows that he is likely to fall victim to getting his own system rooted (at least, according to his own logic), since this transaction should just be terminated.