If you don't have the Trusteer software installed and your computer gets hacked then the bank will wash it hands of the problem: you didn't take its advice, so the problem is yours, not theirs.
In reality the Trusteer software doesn't do much useful: just helps secure the connection and blocks a few trojans. However theres no reason NOT to use it unless you have an old machine. It uses a fair amount of system resources, but any recent machine (i.e. post WinXP) should be able to cope without too much of a performance hit
Its very very arguable as to whether it actually really helps secure the machine, but its not worth the risk of the bank playing hard if something goes wrong