At the time you were filing your application, I believe there was question asking you; did you travel back your COP since you recieved your greencard. I assume that that you answered yes. From that point on, the burden of proof is on the USCIS. They must prove that you have visited your country of origin, and take relevant action.
Why are they sending you this request? My personal opinion is that; first, it is not a good sign. It is solemn determination on the part of interviewing to get to the bottom of your case, and I believe it has to do with your extensive travel. They want to buy more time while they are investigating your case.
What can you do? as fellow members have suggested, you should send coppies of your travel documents. Retain the originals.
at the end, they will have no way of producing evidence that you travelled to cop. therefore, they will ultimately approve your case, but it may longer....be patient and good luck