Once again, details need to be given.
How was this shot? This looks like pull down that you find on a DVX/HVX shot at 24p onto tape. If so this is a import, not an export problem.
I would be surprised if this is on the sequence footage in FCP but you are not using an external monitor and your canvas is NOT set to 100%, which would cause this problem to be hidden from you.
It may also be introduced when you are adding the speed changes to the clip, was again you need to be viewing your FCP timeline on an external monitor, only way to catch these things.
That being said, exporting a ref movie (or self contained movie) from FCP and then taking that into Compressor, gives you more control and in the end better quality.
You should also take the time to learn general terms of our industry, no crime in not knowing what “interlaced” means but our first response should be to look it up and not ask what it is.