A rating? The rating?

I can't make up my mind. I run a small business and each customer is invited to rate their service (give a rating).
If I want to say (discussing one customer):
"When this customer came back with a rating, it was a good one".
"When this customer came back with the rating, it was a good one".

"The" is my default choice here, but a client may or may give a rating (it's not like they are assigned one, which they have to act upon). There might not even be a rating. So "a" could work too? It wouldn't be a mistake?

Thanks.