Signed up for Territory War, but the event disappeared when Setup Phase started.

As far as I know, MindTricks or HighCommand has investigated many of the players who reported signing up and yet being excluded. In all cases except one, the server logs (the official game record) shows those players having never registered at all.

The reason they are asking for screenshots is to see if they can identify a single incident where a player has a confirmed "You are in the TW" entry, and yet the server logs never recorded that entry. A single instance like that could confirm a specific theory about this issue, which would be that the player client isn't always sending the signal to the server.

My recommendation to check yourself is to register early, and then check again the next morning. You checking later will cause your client to pull the registration list from the server, and if the server doesn't "see" you on the list, then it will report you (accurately) as not being in the TW.

That's the intent behind the request. I'm unsure what back-end investigations the software or server engineers are doing, but that's the most likely scenario that's been discussed on these forums so far.