There is no "problem." EEMs distribute the Eucharist, period. And they act at the direction of the pastor of the parish.
You both are conflating something into an issue that simply is not.
If an EEM is bothered by giving the Eucharist to Catholics he feels should not receive, he should STEP DOWN!
I pray they do so en masse.
On the contrary...you have stumbled upon one of the key reasons why laymen should not be distributing the Eucharist, but you seem unwilling to acknowledge same.
It is, at minimum, imprudent to have persons distributing the Sacred Species who do not have the authority to refuse to distribute to a person in the exceptional circumstance when it would clearly be improper to do so.
Again, what about my example above? Should the EMHC just hand over the Eucharist for possible or probable profanation?
This is why the clergy, not the laity, should be distributing the Eucharist.