Is it permissible for a woman to work in a bank, knowing that she only responds to callers' inquiries, in order to help her indebted husband, with the intention of leaving the job once an alternative is available?

Working in usurious banks is impermissible because of the prohibition of aiding in usury, based on the words of Allah Almighty: {And do not cooperate in sin and aggression}, and the words of the Messenger of Allah, peace and blessings be upon him: "Allah has cursed the one who consumes Riba, the one who pays it, its two witnesses, and its scribe; they are all equal in sin." Therefore, responding to callers' inquiries falls under aiding in Riba. The only exception to this prohibition is for someone who has reached the level of legal necessity, which you have not. The responsibility of providing for the household and children rests solely on the husband. If you wish to help your husband, you must adhere to the Sharia guidelines for women's work, one of which is that the work must be permissible.