There’s an old standby for drawing attention in a tavern: get a fight going. If you’re in the right kind of place, you don’t even have to do anything other than wait for one to break out.
This is definitely not that sort of place. Everyone’s too quiet, and you suspect the drinks aren’t even alcoholic. The people here aren’t acting like any drunks you’ve ever seen. It might still be possible to start a fight, but it would be very hard to do without anyone realizing you were responsible.
But the idea’s the same, isn’t it? Get some kind of commotion going. It’s got to sustain itself, though, and it’s got to be hard to ignore.
Maybe… something noisy? Since these people seem to make such a big deal about staying quiet, that could confuse them. Get them wondering who’s to blame.
Well. You do have something that makes noise. A whistle, and a loud one at that. It’s for getting the attention of troublemaking knights. You always keep it with you.
But it’s hard to make sustained noise with a whistle. And you wouldn’t want to be the one blowing it, since the whole idea is to keep attention off of you. Maybe it’s not that helpful after all.
You’re going to need to think a bit more on the specifics of this plan.
Maybe the instructions about not being seen are in reference to persons other than the Silent Ones. Are you sure they’re the only ones in here, and that there aren’t any guards, guides, or shifty-looking folks hiding among them?
If it’s really only Silent Ones, then just go for it and slip around to put half the money under the counter.
Are there any kids around? (even though you’re in a tavern) Even in a city as secular as this one appears to be, kids probably still behave like, well, kids. If one of them got their hands on a whistle, they would probably blow it. This is kind of a convoluted way of going about it though, so maybe, maybe not.