Is it permissible to make purchases using an Islamic bank card that reserves the money and only debits it after one day, knowing that the purchases are made from companies that have accounts in interest-based banks?

There is no objection to using bank cards for withdrawal or purchase, even if the amount is held and only debited after a period of time. This is permissible even in transactions that require immediate possession, especially since the bank entry is considered a constructive possession. There is no objection to purchasing with this card in Western countries, even if the payment is made through an interest-based bank, because the purchase itself is not an interest-based transaction, and the bank is merely a means to collect the price.