Well it seems to be clear that the website is expecting something to be running on your machine it can connect to through the browser, e.g. some form of authentication perhaps (it is listed as "Módulo de Segurança CAIXA"). If you aren't running that software, then the localhost loopback connection will fail.
This isn't something in particular to do with Pale Moon, though, since it's some kind of interaction with a third-party piece of software (the named CAIXA security module) it seems to expect to be present. it lists "Não localizado. Para acessar sua conta, baixe e instale o Módulo de Segurança CAIXA clicando no botão CONCORDO." to install said module.
In other words: if you want to use internet banking with them, you have to install their prerequisite software and make sure it's running.
Off-topic:P.S.: What's up with this "InteR_n:et---BaNki:ng----CAIXA:" pseudo-leet way of writing a title?
