Log into CORE and go to your listings tab. Click on the listing that you need to change the MLS synchronization on.
Click on the data synchronization link (highlighted in yellow above). This will open a box and you can select what you do not want to not sync with the MLS. Uncheck that box. (Remember, if you select to not sync with the MLS you will have to manage the listing(s) on your own since the listing(s) will no longer update when the MLS does). Then click on update sync settings.