I had a few of those eggs with my hens, too. I increased their calcium by giving them the oyster grit you get from the store but I also do my SURE way; that is to save the egg shells then put them in the oven on about 170-190 degrees for an hour or 2 or so. Then, grind them to an almost powder...
I've had a padlock on my run since day one and I've NEVER regretted it ...even when I've forgotten the key and had to walk back to the house to get it! Whether someone's intent is evil or not, I just don't like anyone messing with my property: animal, machinery, plant, or anything else.
I've recently been getting them from my hen, too. I think it is from my Buff Orpington, as well. I know it's just calcium deposit but I wonder about the mechanism for it. Such tiny beads of calcium. Is this how it is formed on the liquid part of the egg as it passes through? If so, how does it...
I release mine into a small chicken tractor. I have a fence tunnel for them to run through to get to it, then I can pull it to wherever I want them then back to the run in the afternoon. They love it. Maybe if I had a totally enclosed backyard but we have too many stray dogs, cats, traffic...