Have I ruined my door??

I have a fiberglass door in my garage. The lock broke and had to be replaced. The pictures show the replacement. The plate the bolt goes through has to be recessed down in to the edge of the door. My door did not have a recess so I made one. That was probably a mistake. There are two screws that go through the plate and into the door. They are probably not going to hold in fiberglass, will they? Is there a certain type of screw for fiberglass. Or should I try gluing the plate in place? Or is the door ruined? Thanks.