Is it permissible for me to enter and audit amounts that have been spent with a usurious bank credit card belonging to the employer?

Firstly: Using a credit card issued by a Riba-based bank involves two prohibitions: The first is engaging in Riba-based borrowing when the customer withdraws money they do not own, and the second is the commitment to pay a late fee. Some scholars have permitted its use out of necessity for those who are highly confident they will not delay repayment, but cards free from prohibited conditions are preferable.

Secondly: It is impermissible to write or record Riba or assist in it, due to Allah's saying: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression), and because the Prophet, peace and blessings be upon him, cursed the one who consumes Riba, the one who feeds it, its scribe, and its two witnesses. Therefore, if the company owner withdraws money without a balance, it is not permissible for you to record it. However, if he withdraws from his balance, there is no harm in recording that, and he should be advised to cease dealing with Riba-based banks.