Check the properties of the clip in the Motion tab. Double click the one in the timeline, NOT the one in the bin. Is the scale at 100% or something smaller?
If you captured the screen at full rez and it’s scaling it down to your video size, it may be that it’s being squeezed too much and that’s what’s causing the problem.
If you look in the Motion tab for the clip on the timeline and find that it’s set to something like 15% size then it might make sense to either blow it up larger (thus losing the edges of the screen) or try to re-record it with the screen set to 800×600 so that it doesn’t have to be re-sized as much by Final Cut.