On the photo that you have provided. The center is a magnet. Around the magnet is a voice coil former. They have slid paper in place between the magnet and former to make an even gap. This is the voice coil gap. Without that gap, your voicecoil will rub when the woofer is working. This must be done. You put the shims to balance this gap, You replace the surround. Then remember to remove the shims before you re glue your dust cap back on. For what ever reason. I get the idea that they had a small dust cap, and another larger dustcap over that. If they did that, then yes, put the second (larger) dust cap back on. It can affect the mid range as well as the bass performance if it has much weight.