Fisherman, the "brief" would be the written legal argument by WTBTS why the original Court decision on document disclosure is wrong.
I haven't been following this case closely, but I find it very strange that WTBTS hasn't filed a brief. From memory there could be a lot of money at stake in this case because there were a large number of victims in the relevant congregation. If WTBTS doesn't file a brief, WTBTS would have no argument to not pay the accumulating $4000 per day. Perhaps WTBTS is trying to string it out as long as possible, and hope to settle.