Is this a case where the could be used to indicate whether it is 'They" or "them" who is being mocked?
There seems to be something missing from your sentence. I don't understand your question.
Nor do I understand the distinction you are trying to make in whether it is 'they" or "them" who is being mocked -- "they" and "them" is the same thing, isn't it? Third person plural?
One could see an ambiguity in the English that persists into the Klingon: one might wonder whether A mocked B because of B's religion, (QIp Qunqoqraj!) or A mocked B because A's religion calls for a solid hour of mocking once a week in order to keep the divine blessings flowing.
If they and them are the same entities, because their faith calls for a little self-mockery, then lalDanchajmo' vaq'egh or lalDanchajmo' vaqchuq depending on how the sacred rite is conducted.
On the other hand if the self mockery was because of the religion of another group --heck there could be a third group involved --we'd need to use more than pronouns to explain the situation, same as English.
'anDorya'ngan lalDanmo' torgh lurveng je vaq martaq mara je.
Martok and Mara mock Torg and Lurveng because of the Andorians' religion.
pIj Qatlh lalDan Soj.
My answer for this was "Because of their religion, they were mocked." It's apparently wrong. Is this a case where we need to specify that "they" verbed "them", even though we don't know who either of the parties involved are? If so, is there any way to tell when that's specifically needed, or is that left up to context as well?
In English, "they were mocked" is a way to specifically leave out the subject. "They mocked them" still leaves the subject somewhat ambiguous, but it at least specifies some sort of subject. Klingon also has a way to specifically leave out the subject using the -lu' suffix, so chaH vaqlu' would be equivalent to "they were mocked". There could be a situation where no subject pronoun is used at all in the Klingon and you have to assume that the subject is known to the speaker and listener, as in the complete sentence vaq. You would still add in the pronouns in the English ("They mocked them."), because when known by the speaker and listener, they are required in the English, but not in the Klingon. But in this case, a specific pronoun is given in the subject place (chaH), so it is even odder for it to be left off of the translation. Assume that if there is not a -lu' suffix, you must always give a subject pronoun.