First - let me just say, I love Lee Precision products ... especially their collet neck sizer. That being said, I would never claim they are the "high quality" choice ...
I had rings like this appearing upon FIRING as opposed to resizing ... it was due to a rough chamber that needed to be polished. If this is occurring upon RESIZING, then I'd bet this is due to a rough die that needs to be polished.
This is a tool that might help you out not only for this die but other similar needs (i.e. chamber polishing, etc) ...
This hone features a twisted steel wire shaft with abrasive globules on flexible nylon filaments. It allows you to remove any imperfections or machining...
ads.midwayusa.com
Sorry to post a link from the pirates at midway ... but google it and I am sure you can find it from a seller that has some honor in their bones ...