The tax on covered items and the tax on non-covered items will be tallied separately.
In the past, they used to give entirely separate checks for covered and non-covered items, but now they'll just zero out the covered items (which puts the tax on those items to $0 as well) and tally the tax for the non-covered items.
So, for example, when you first get the check, it may look like:
Appetizer..... $12.00
Entree..........$24.00
Dessert........$9.00
Soda............$2.99
Beer............$7.50
Subtotal.......$55.49
Tax.............$3.61
Total...........$59.10
After you give them the KTTW card and fill in the other amount, it'll look like...
Appetizer..... $12.00
Entree..........$0.00
Dessert........$0.00
Soda............$0.00
Beer............$7.50
Subtotal.......$19.50
Tax.............$1.27
Total...........$20.77
And at the bottom there will show two transactions which should look like:
DDP Purchase: $0.00
Room Charge: $31.77 (This includes that other amount of $11)
Note that "Room Charge" may be cash, CC, or whatever you end up using. There's also a lot more information on each transaction, but it's not important for this.