You can read many forums posted back before 2009 even, when this software was being installed on Vista machines. Yes ok so Vista already had a bad reputation so pretty much any software company was able to say that it 'helped with security' but the truth is, it simply doesn't and this is for the one main reason that you are giving this administrative privileges to start monitoring secure transactions of your web browser.
The real problem is the Bank employees are simply clueless to software/security and are only pushing what products they are told to push. Best to consult with your computer tech if you are unsure of any software you are being told to install, for security reasons!
What you should be doing is using anti spyware/malware scanning programs like Malwarebytes and CCLEANER to keep your system free and clear from the nasties.
You can read more through the following forum and web links if you don't believe me.
A Closer Look at Rapport from Trusteer
