From the FAQ:I wonder if they'll take my letter instead. Will be asking about a card tomorrow though.
HOW DO I PROVE THAT I’VE BEEN VACCINATED?
Any qualified guest needs to show their COVID-19 Vaccination Record Card to redeem the COVID-19 Vaccine Offer.
DOES MY VACCINE STICKER QUALIFY?
A COVID-19 Vaccination Record Card needs to be provided to receive the offer. A sticker stating the guest have received a COVID-19 vaccine does not qualify them for this offer.
The trial letter is interesting. You could probably argue it's as valid as the card. I bet they just give you a donut. It's not like this is some higher stakes thing where giving you the free donut risks exposing someone. It's a coupon where they didn't do the ad copy. The FAQ seems to draw the fake qualification between people willing to show a sticker and those willing to create a fake vaccine card. Just like a real coupon wouldn't be accepted if it wasn't an original. Assuming it was even a paper thing and not an email on someone's phone. My guess is the front line worker would accept an official looking letter. Since, who's going to go to the trouble of faking that for one donut. They might as well assume it's real, which in your case, it would be real.
Assuming you want the donut and it's not to far out of the way and you have the letter on you.
