게 털다

shake off, dust off

An adverb in "-게" plus 털다, shaking something to knock stuff off it. The literal use is here — smokers tap their cigarette like this, brushing dust off a desk — as is the extended "get it out of your system": how do you shake off stress, once he's got the talk out of him. 털다 also means to clean a place out or make off with the contents, and two lines use that: walking off calmly after emptying the place, and "how are we going to move two trillion?" The adverb before it tells you the manner, not the sense.

Register: casual