If your source video is DVD/MPEG-2, DV, DVCPro or any codec that starts with DV - set the Field Dominance Override to Lower First. Everything else, set the Field Dominance Override to Upper First. Select your clip in the Event browser and you can find the Field Dominance in the Info Inspector > Settings. If this setting is set to Progressive, then FCPX will not conform interlaced video in a progressive project... because it thinks the clip is already progressive. If the setting is set to "Off", then FCPX will try to infer by the clip's codec what the status is — it doesn't always make the correct guess.
Since you're dealing with a cartoon, you may also have a frame rate issue. Cartoons are generally created with around 15fps (some as slow as 10!) and if your cartoon video has been "normalized" (or conformed) to 30 fps (by which I also mean 29.97i) then that interlacing might be burned into at least every other frame (there may be no "fixing" it without the original.)
Your video is no longer available on Dropbox and I missed being able to download it and inspect it, so, what are the specs of the original video? (Codec/Format info - not "container" info like mov, mp4, etc.)
