It depends. If you use a private VPN, they will have no way to detect it. For example, if your company hosts a private VPN to allow you to access their internal network, and if you use it and then connect to the banking service through the corporate proxy, the banking service will only see a connexion from the corporate proxy of your organization, which is no surprise, and have no way to know more.
Things are different if you use a well known public proxy. Outgoing IP addresses of those proxies may be known, for example TOR endpoints are published. In that case, the banking service has no way to know your actual IP address nor where you are, but they can know that you are hiding that behind a VPN. As it is what most attackers would do to limit the risk of being caught, it might be enough for the banking service to see it as suspicious and require an additional authentication procedure or reject the connection.
To use a real life analogy, using a public VPN to connect to your online bank is not different from hiding your face behind a mask to enter your physical bank office. And I am not sure of how the guard will react...