This book was about two girls who are taken to the future because the future's IQ population is dropping. An organisation takes smart people from the past to the future to boost the IQ's of the future's inhabitants. However, they take them moments before they're meant to die. A second organisation thinks it's wrong, as if the person declines, they're returned to die.
Could it be Millennium by John Varley?
Millennium features a civilization that has dubbed itself "The Last Age". Due to millennia of warfare of every type (nineteen nuclear wars alone), the Earth has been heavily polluted and humanity's gene pool irreparably damaged. They have thus embarked on a desperate plan; time travel into the past, collect healthy humans, and send them to an uncontaminated planet to rebuild civilization.
It's not to boost IQ, but to have healthy humans in general, who they take moments before they would have died. In the book it's from an airplane that is about to crash. The summary doesn't mention a second organization that is against that, though.