What you are seeing is a morié pattern (http://en.wikipedia.org/wiki/Moir%C3%A9_pattern).
Proper wardrobe selection is probably the best way to handle things, BUT you have your interview shot already.
You might explore doing a duplicate of your Clip, and placing it above your original footage. You would then add some Blur to the duplicate. Then create a Track Matte Key, to restrict the Blurred footage to just the shirt. Note: if he/she had a tie, things get a bit more touchy.
Maybe someone else has some neat tip, that I am not thinking about.
Try Flicker Removal in the Field Options.
Basically this occurs when the chroma and luma information gets scrambled. It's something that I used to see happen constantly when dealing with RCA cables and Composite (bnc) style video cables. Like Bill has already stated in all honesty people just need to avoid wearing clothes like this. Because if it is going to be aired on TV it will almost for sure end up appearing this way by the time it goes OTA and viewed on the viewers TV, or after it's ingested into a playback server and compressed yet again. Or if it's watch at home on someone's DVD player and viewed over RCA cables the signal will once again get scrambled.
Although I realize this might not apply to your own scenario I just figured I'd mention it. Because even if you apply a fix for this generation of encoding it's likely to show up again when it's viewed on DVD or if it's going to be aired on TV or put on you-tube or compressed again at some point. Because when compression of the signal is applied the chroma and luma information will get scrambled. There really isn't much you can do about it to make it go away. (Permanently anyways)