Leave the padding there. It is used to ground the shield.
Your problem is with installation.
1. Make certain that the shield is securely fitted into the case opening. You need to press all the way around so it fits fully flush.
2. Installing the motherboard ideally takes three hands. one to hold the case, one to push the motherboard into the I/o shield, and one to put the first motherboard screw into the hole nearest to the I/o shield. (a #2 magnetic tip screwdriver helps)