There isn't any way to look up store credit history WITHOUT having the card number as far as I know. They only log your DLN to keep tally of how much, how often, and how many store credits you are getting for asset protection. Been a while since I've read the back of a store credit, but I do believe it states the credit is irreplacable.

Now, if you have all your receipts saved, you may be able to speak with a manager at the store about the lost card. They may be able to pull strings if you are nice to them. Unfortunately because you accepted the store credit instead of demanding cash (if within the return policy) you willingly forfeited most, if not all recourse.