[Were they to be told] the purpose of the study, the participants might find it difficult to answer the questions spontaneously.
Why can’t you replaced the bracketed phrase with “by telling them”? If you keep the sentence the same, wouldn’t it have to read, “Were they to be told the purpose of the study, the participants might have found it difficult to answer the questions spontaneously”?
It’s the subjunctive mood (projecting to the future), not past tense.
Rephrase it to see:
“If I were told, I would find it difficult.”
Can you see how the finding is in the future, as compared to the telling? If I were told right now, I would find it difficult in the future. Same with “might”; it’s still futuristic, but a little more uncertain.
“By telling them” creates a misplaced modifier, for one thing. Who’s telling them? Where’s your subject?
Your example sentence should be “Had they been told…” to match the latter part.