I have to disagree with Dave, the tiles are there to weatherproof a roof, the felt is there to waterproof it. Some tile are porous and will let water through; this is why the felt is lapped in to the gutters and causes damp problems when it slips behind and collapses in to the cavity.
The only sound way to effect a repair is to remove the tiles and replace the felt.
Gearbox
March 2010