I assume you are asking about que (Spanish) and not that (English)
In Spanish, the biggest factor is a change in subject between the two clauses. If there is no change in subject, then usually the que is not needed and the next verb is in the infinitive. If there is a change in subject then both verbs are conjugated.
Quiero comer ahora.
I want to eat now.
(the wanting and the eating have the same subject (I)
Quiero que comamos ahora.
I want us to eat now. (Literally, I want that we eat now)
In the sentence of this exercise there is a change in subject.
It is a pity. Subject "it" , an impersonal subject
that they lost. Subject they (ellos)
I don't think pierdan is right. The English clearly refers to a past event (lost, not lose). The present subjunctive ... pierdan ... should apply only to a present or future possibility. In this case the losing has already happened, it is a fact. There is no uncertainly, but Spanish requieres is to be either hayan perdido or perdieron because it is a past event about which you are expressing an emotional reaction.