It seems strange that the website which provided the image and licence cannot provide details of your transaction. If they could, that would obviously support your defence. Are they denying that the transaction took place, or merely that they have deleted the details? If it's the latter, how does the copyright owner know that you don't hold a licence? Could the licence have lapsed since it was a obtained a long time ago?
But without the licence and any evidence of the transaction, I'm afraid you will find it very hard to defend yourself, either in trying to settle the claim or if the matter does go to court. The best you can do is see if you have any secondary evidence such as a credit card payment to support your version of events.
Are you sure you bought the image from a genuine company? There are many fake companies out there that purport to give Licence for work that they don't actually own or have permissions for.
If you did buy from a genuine company, then they should have a record of it. Businesses are required to keep business records for 6 years in the UK and so they should be able at the very least to confirm a payment within this time frame and most will have Licence records going back much longer.
Check your bank statements for the transaction and check your emails for both the financial transaction through a card handling payment service as well as emails from the agent that sold you the image. If you can at least find the payment date then a reputable agent should be able to tie that to a licence.
Beware that your original licence may have been time limited and since expired. Most licences are sold for a specific period and exceeding that period is an infringement.
For future orders, be very careful to keep copies of permissions and transaction records.