How do the odd-or-even verifiers (cards 5 and 33) work when they return a check?

Question

Accepted Answer

Each one checks a parity option, odd or even, for one digit, and the option it knows can differ from puzzle to puzzle. A check means the tested digit's parity matches the solution's. Change one number at a time to find which digit and which parity the verifier knows.

Turing Machine

How do the odd-or-even verifiers (cards 5 and 33) work when they return a check?