Here is what I can see from this whole process.
In December there was a card fee and that got paid, so your card balance would have then been zero. In the contract you have with Cardlink there is a monthly fee of just under $3 whether you use the card or not.
You have then in December cancelled the Direct Debit, have not informed Cardlink of this and also you have not cancelled your card either.
From a Direct Debit perspective, any subsequent Direct debits will never post to your account as the bank has no authority to post them to your account and these would have been dishonoured with either a reason code of 01 Payment Unauthorised or 05 Authority Cancelled. This dishonouring code tells Card Link of the status of their request, so that is the bank informing Card Link.
So from a banks perspective here, whoever this bank is has done nothing wrong and for every attempt that Card Link make, tells them by way of dishonour the reason for non payment.
You have advised insufficient funds was what you were being told by Card Link, I can not see where that would have come from, you could ask your bank or Card Link for the dishonour reason code that was being returned, but honestly it is semantics in relation to the payment, it is still not paid.
In February card Link did advise yourself that payment was rejected by your bank and at that point you should have investigated further. You say that they hadn’t been notified by the bank, well yes they have hence why they are saying the DD was rejected by the bank, that is because the bank has dishonoured the attempt and will dishonour all other attempts.
To sum this up, your bank (whoever that is) has done nothing wrong and has adhered to all of the Direct Debit rules the banks must operate under. Card Link did inform yourself that payment has been unable to be effected, you also then re used the card knowing that this would then incur a cost that you had to pay for. Yes you may have forgot that you cancelled the Direct Debit, but Card Link informed you by way of text in February that they could not Direct Debit your account.
Not sure what other debt communication you did or did not receive between Card Link and yourself, and I can sympathise with the level of fees being charged for non payment, however as you say it pays to look at all of the terms and conditions, should you not meet your obligations in paying the debt.
In having this difficult conversation, there has been a bit of responsibility on yourself that had you acted earlier would have saved yourself a whole lot of financial stress and trouble.
I hope you could come to some sort of agreement with Card Link, around the re payments, in relation to the Direct Debit component, there is nothing untoward here and is between yourself and Card Link.
I wish you well Ford and I am more than happy as always in BNZ Community to answer any questions where I can add value to any subject that I have a good understanding.