Sounds like your footage was shot either regular interlaced or with pulldown. It sounds like you are describing interlaced lines of video displayed progressively.
Is there a reason you are trying to cut it in a 23.98 timeline? What is your delivery format?
If the footage was shot with 3:2 pulldown, you can reverse telecine the clips in Cinema Tools and make it 23.98 progressive and cut away.
If it’s interlaced, you can apply a deinterlace filter, and depending on the setting, you’ll either double the fields or create a motion blur because of the difference between the fields.
Also, check your field setting (lower/upper) between your clip and timeline to make sure they match.
Matt Small
Denver, CO
“If it was easy, everyone would do it.”