Please show us the response you get as their clarification and requested information when it arrives. As I have already predicted, Wise are going to instruct BW Legal to file a claim. Let them.
Once a claim has been filed, you will be in a position to defend and put them on notice that they will be required to provide strict proof that they sent an NtH. Later on in the process, they will have to provide evidence of what they allege they sent. You will be able to see any NtH. They will also have to show that they also sent the necessary copies of document with that NtH in order to be able to hold the Hirer liable.
It is all months away. If you do want to see what information they hold about you, then you can send them an SAR, but not before the claim is filed.
In our defence, you will only be answering the woefully inadequate PoC which may not even state the cause of action, another arrow in your quiver to use against them.