"Unrequested" would make more sense to me in this context. In conversation I would expect "We don't have to give them information they didn't ask for." or "We don't have to give them any(thing) more than they asked for."
I hesitate to say "wrong" but in this case I would say that "give them not requested information" is an incorrect word order. Tricksy's word order switch makes it acceptable. It still sounds unnatural to me, even with the change in word order.
"Not requested" in this context sounds as odd to me as:
"I just finished reading my not read mail (instead of unread mail)."
"I have some not finished business with you (instead of unfinished business)."
"You appear to have some not reported income (instead of unreported income)."
If there is an "un-" version of the word I would always use that as an adjective rather than sticking "not" in the sentence.