The Tooga are the only group of people allowed to enter the town. They trade goods between Glie and everywhere else. They are not allowed to speak to or associate with the townspeople, but communicate through sign language with Washi.

The Tooga are connected with the Haibane Renmei, but it's hard to tell just how deep the connection goes. They both use the same sign language, and their garments have many similarities, so it could be that the Tooga are simply the mobile section of the Renmei.
I do notice that all the ones we see seem to be fairly young. At least, they give that impression.

The Tooga get very little screen time in the series. Other than their minor appearance in episode 2, we only ever see them again when they rescue Rakka from the well. There's not a lot to go on for speculation.
It seems clear that they're connected with the crows in some way, though. They and the Tooga are the only ones allowed to enter the city. If they could communicate in much the same way Rakka does, this would help explain why the Tooga were able to find her.

The main question about the Tooga is who they are. Are they failed haibane, like the Renmei is? If so, the number of haibane who fail their trials must be fairly high, since there's quite a group of them.
If the Tooga are also failed haibane, it could be that there are multiple stages to a post-haibane life. The first would seem to be with the Tooga. They seem younger than the Renmei, and certainly younger than Washi, even as he was in the flashback section of episode 10. Perhaps they're sent out to learn before they take up permanent residence.

What's more interesting is what the Tooga implies about the world outside of Glie. Either the Tooga are engaged in a massive filtering project (on all those books and other goods they bring in to the city), or there are a number of cities like Glie around, which the Tooga travel between.
This could tie in with the above speculation as well, as it would allow failed haibane to be removed from the temptation of talking to those they knew before. I am assuming here that the failed haibane remember their lives as haibane, which Washi's comments seem to indicate.