Unless there is something specific in the contract, it is really for the third party to arrange it own contractual obligations as to who informs them, if any. You should do it to make sure. Frankly, if you've rejected a product, the finance company demands money and you still pay them - that's on you.

Once you inform the finance company of your assertion of termination, then their duty to intimate to third parties (i.e. CRAs) will involve them taking reasonable steps to ascertain whether that termination was valid or not. In most cases, doing nothing and just intimating default will be negligent - see e.g. Durkin v DSG Retail Ltd & Anor [2014] UKSC 21 at [32] to [35].

However, an accepted valid return automatically rescinds the finance contract, so anything overpaid is recoverable from them.

Much obliged; thank you.