There is "a way" for them to delete... they simply report a deletion to the CRA. That is not illegal or improper.
However, it is against their reporting agreement with the CRAs, which explicitly instruct furnishers not to delete based on payment of the debt.
To argue with them that they are incorrect in asserting that they "cannot" delete is a confrontation. They can simply refuse to delete without any reason, and with their reporting agreement not to delete on that basis, you have a confrontation with no clout.
I would try to find a higher-up who might grant an exception as opposed to aguing with the party who is now asserting they cannot delete.
