If you have the name and description of the folks you interacted with I don't know that you absolutely have to have a business card. My 'auto-drive' with a bank shop is to get a card and get collateral that they offer to discuss product with me. If I have it in hand I may as well throw it on the scanner. If I have it scanned I may as well attach it with the invoice to email it all to the scheduler. If they wish to discard it, that is fine. Certainly before they had a website to report jobs on line the business card and collateral were a requirement.
I get the cards anyway, scan them and keep them for a record.
What is also easier is when you get in the habit of doing or noting certain things, then it is easier not to forget. I always get a business card, even when not mystery shopping. On shops, I always note the in and out times, even when only the in time is required. I observe the characteristics of a person for the description as much as I can since some only want a bare minimum and others would prefer to have a body scan if they could.