Is it permissible to work for a company that operates in a permissible field, but deals with interest-based banks, knowing that my job responsibilities include handling data and information related to these interest-based dealings, such as taking backups of them?

Working for the aforementioned company, even if it involves copying files related to its dealings with usurious banks, is not forbidden. This is because the copying of these files is not intended as an primary act, but rather as a subsidiary one, and what is excusable in a subsidiary act may not be excusable in a primary one.