Your bank could put a line at the top of your statement that reads:

SPECIAL HAPPY NEW YEAR MESSAGE FROM FACEBANK $0.00

and then come February they realise they look pretty stupid so they take it out of the statement (web page). No one would care too much.

Nope, that would violate the agreement made between you and your bank.

So you think someone removing something he posted is the same as someone taking money off someone?