L112 128H woofer vent / magnet foam

Greetings from a new member!
I am trying to restore a pair of JBL L112 speakers that are in excellent (near mint) physical condition. The woofers are in need of a refoaming. I've done the research on this board on the merits of refoaming vs. reconing, but am looking for further guidance on a specific issue:

There is some kind of foam plug in the back of the magnet structure. Foolishly, I stuck my finger in there and touched it, and it crumbled just as the surrounds have crumbled. I'm not sure what to do about this. I saw one thread that mentioned that the crumbled foam might end up in the voice coil gap with negative consequences. Should I just pull the foam out completely? What was the original purpose? Do refoaming kits supply a replacement for this part? Do I need to have the driver reconed to properly restore this part as well?

Any tips and hints would be greatly appreciated. Thanks in advance.