Mark, there is no explicit dampening to smooth out pitch variations in ETDs, but dampening does occur implicitly. In TuneLab for example, the Spectrum Display is updated about 3 times per second. On each update, the pitch of the string may be varying during that 1/3 of a second time period, but the spectrum calculation inherently forms an average picture of the pitch during that time period. Going from one update to the next, there is no averaging. So any pitch variations that occur slowly enough to be different from one update to the next will be reflected in a change in the location of the graphical peak.
The Phase Display is a little different. It doesn't actually measure pitch. It measures phase. A changing phase is equivalent to a pitch offset, much like aural beat detection. That display updates at a faster rate than the Spectrum Display, so it is more sensitive to shorter term pitch variations. An unstable string will result in an jiggling pattern. However the real job of smoothing the Phase Display happens in the eyes and the brain of the user. Even if the display is jiggling, your eyes can discern an average pitch offset by tracking the overall movement of the pattern. The longer you wait to make this determination, the more smoothing you are applying. But the ETD doesn't do that smoothing. You do.