I can explain this! Although I am relatively new to Italian, this is identical to Spanish:
"Ciò che loro mi hanno detto non è vero." Best translates to: "[That which] they have said [to] me is not true"
"Ciò" is used to indicate a thing, possibly an abstract noun. In this sentence it therefore references "that which" has been said to the speaker.
In Spanish "Ciò che" is "Lo que". Lo means "it/he/the" depending on context.
I would just remember "ciò que" separate from its literal meaning for now and treat it as "that which"
@Italian speakers: Am I correct in this assumption?
The first time through the printed words came up along with the spoken sentence. I didn't have to rely on the voice. Then when it came up a second time (after I flunked and repeated), there were no printed words to follow. And I agree that "detto" wasn't clear. To me it sounded like "bitto."
The “is not true” refers to it being not true currently, not whether it was true or not at the time they said it. It is completely valid to have this sentence be partially in past tense and partially in present tense. Assuming Italian makes that distinction too, it is not correct to use “was” in the translation, considering that the original says “non è vero” in the present tense.