First of all, I turned my hook around on the fabric tab so it engages the forward edge of the hole. Then...
If you look at the fabric carpet there are two threaded hold-downs on the forward, outer corners - the one on the left is a plastic disk and the one on the right is a steel "D"-ring to attach the child seat (both M8 thread). The plastic fastner comes out easily by fingertips; it will take a T40 Torx bit and some strength to initially remove the machine screw in the "D"-ring. Once those two fasteners are out there is a lot more available movement in the carpet, and it is actually a lot further out of the way. The fasteners can both be put back finger-tight. I have on order a second plastic fastener to replace the "D"-ring and screw (P/N A000 991 2795, 86¢).