How do I remove my payment debit card details from the card that is not working?

Add a new one before you can remove the old one.

Know it here --> If your payment method is declined in the App Store or iTunes ...

Check the following

1. The payment method that you are adding is of the same country as that of App Store Country on your iPhone
2. You have valid payment plan / debit / credit card from an authorised bank from the same country
3. Payment methods that you can use with your Apple ID - Apple Support
4. Learn more about family purchases and payments.
5. Please check if your Debit/Credit card is valid internationally

If you can't choose None when you edit your Apple ID payment information

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing