First, the priest should make it a priority that his congregation knows and understands the restriction. Good, basic catechesis is needed and often desperately lacking. The homily is a good time to hit on those subjects, though I have also experienced in eastern rite churches the priest calling the community together after the liturgy to hold a Christian Formation class as a refresher every so often.
If the priest doesn’t know and has no reason to suspect, he isn’t responsible. But if he is given reason to suspect he should ask and if there is a condition then he should council them and carefully explain why they shouldn’t take communion and why he will not give it to them. The spiritual state of his congregation is the priest’s responsibility.
How can ONE priest be responsible for the spiritual state of an entire congregation? Or for the spiritual state of even ONE person? Each person is responsible for his own spiritual state.
But, I get your drift and don't disagree.