Just cleaned up three dozen of these for sale. I clean, coat with food safe mineral oil, and refrigerate mine. You *can* leave them on the counter but they do age faster. Still better than store bought! I just won’t put unwashed eggs in my refrigerator. 
Discussion
we leave ours out, unwashed until we use them. They never last long enough for me to know how long they'd last otherwise, yum. I've never used mineral oil though, interesting.
I sell my excess so I want to prolong their freshness. Plus, the chickens share space with the ducks and sometimes it gets muddy in the run. The mineral oil is to help reseal the shells after washing. It's a food grade that you can use on butcher blocks or soapstone counters, etc. If I just had a couple layers I wouldn't worry about it.