“The other reason to refuse adjudicating is as a penalty to the litigant, who was wrong to turn to the civil court,” continued Rabbi Dayan. “This reason is accepted by most achronim. Certainly, if the plaintiff was awarded a small payment by the civil court, but is entitled to more according to halacha, beis din should not impose the additional amount according to the Rama. Some maintain, though, that the defendant still has a personal obligation to pay what he owes according to halacha; others say that he does not, since the plaintiff forwent his right.” (See Nesivos 26:2; Aruch Hashulchan 26:1; Tashbetz 3:68.)
“So what should I do about Mr. Cohen?” asked the secretary.
“If Mr. Cohen does not want to appear, we cannot demand that he come,” concluded Rabbi Dayan. “Nonetheless, some batei din will accept the case if both parties want to, even after litigation in secular courts.” (Shevet Halevi 9:287)