We had no problem with a walk up on the 20th. It's a great restaurant, with great atmosphere, and we were really pleased.
We got there pretty early...just before they opened around 11 am and asked for the "Owner's Table" on a friend's recommendation, and we got the sweetest table in the house.
The staff told us that same day reservation/walk up is all they are doing right now, and for the next month.
As of today, you can only reserve same-day lunch (up to 2:30) through the app or website. I'm frustrated you can't still make same-day dinner reservations. I wish they would make up their mind on this place.