Agreed. Touch the route line and hold your finger still for a moment before starting to drag. iFly will respond as Mark described: The route line turns green, with crosshairs over your dragged waypoint. When you lift your finger, you'll be presented with a menu of waypoint options, including the exact Lat/Lon you dragged to, plus nearby charted waypoints you may have intended (GPS fixes, airports, navaids, etc.). Selecting one of those waypoints will confirm your rubber-banded change. Otherwise, selecting "Cancel" or touching anywhere else on the map will revert back to the route as it was before you disturbed it.
If your aim is good and you're touching the route line, it only takes a very short moment before it transitions to rubber-band mode. 100ms? 150, maybe? In my experience, the behavior is very comfortable/intuitive.
If you're using an iFly device, especially an older unit, it might be that the screen digitizer grid has drifted, with the result being that where your finger is touching may not exactly match where the device is registering the touch. In that case, you could try recalibrating the digitizer to see if that helps. (Very old units can have uncorrectable drift that requires screen replacement to repair.) You can test for digitizer drift by touch-and-holding your finger to the map at various places around the screen. iFly will draw a circle of dots around your fingertip to acknowledge the touch. If your finger is not centered in that circle, the digitizer has drifted. Note that different regions of the screen can exhibit different amounts of drift--it's common to only see a problem near one corner of the screen, for instance.
The touch technology of the iFly devices is also different from that of most other touch devices used today, and you may get better results using your fingernail or a stylus (or a pencap or a pencil eraser) to make a more precise touch input, rather than the pad of your fingertip.