What is the effect of wingspan on wing stiffness?
Limit cycle oscillation is a fancy term for flutter with constant amplitude. The limit cycle is an attractor, meaning that the frequencies and amplitudes of a range of oscillations will converge to the limit cycle oscillation as time progresses. One example can be witnessed in this video.

By removing the wingtip, GE could raise the bending eigenfrequency of the wing, like you make a pendulum swing faster if you shorten it. Adding a heavier engine before certainly reduced the eigenfrequency, so the shortening was a way of compensating for the changed dynamic characteristics of the modified wing-engine combination.

Wingtip removal does not make the wing stiffer, only larger spar caps, a thicker spar or employing a stiffer spar material would. Stiffening the wing spar would raise its bending eigenfrequencies, and removal of the wing tip would do the same by different means. I guess the author wanted to express that bending frequencies were raised but picked the wrong explanation.