The Replay Official cannot initiate a review of any ruling against a team that commits a foul that delays the next snap, such as illegally throwing the challenge flag. For your reference, the same situation happened on a turnover last week in the Arizona-Atlanta game.
The NFL Rule Book (page 89) states:
Replay Official’s Request for Review. After all scoring plays, interceptions, fumbles and backward passes that are recovered by an opponent or go out of bounds through an opponent’s end zone, muffed scrimmage kicks recovered by the kicking team, after the two-minute warning of each half, and throughout any overtime period, any Replay Review will be initiated by a Replay Official from a Replay Booth comparable to the location of the coaches’ booth or Press Box. There is no limit to the number of Referee Reviews that may be initiated by the Replay Official. He must initiate a review before the next legal snap or kick and cannot initiate a review of any ruling against a team that commits a foul that delays the next snap. His ability to initiate a review will be unrelated to the number of timeouts that either team has remaining, and no timeout will be charged for any review initiated by the Replay Official.