Rennie, who plays for the Newtown Jets, has also been hit with a one-match ban and is set to miss this weekend's must win clash with Tonga at Middlesbrough after being booked for a dangerous throw.
Ireland prop Jaimin Jolliffe will miss the game against New Zealand after unsuccessfully contesting his ban for a high tackle, while teammate Liam Byrne and Fiji's Tui Kamikamica will also miss the final round of World Cup pool matches.
With Byrne suspended for two matches on separate dangerous contact charges, the Wolfhounds challenged Jolliffe's ban in a desperate bid to have him available for the must-win match against the Kiwis in Leeds.
Byrne also received a caution for contrary behaviour.
Fiji team-mate Taniela Sadrugu, who plays for the Cowboys, received a caution for dangerous contact.