I was able to take one of them home. As I suspected the coating had been compromised and was definitely breaking apart and being broken down in my finger! I used a macro lens for my phone and got a closer shot. Keep in mind this disc is only 3mm in diameter.
Still, it's a very good thing I got them removed before they broke apart or infection occurred. The doctor and nurses kept asking "are you going to get more put in?"
The answer is "no."
The fingers are healing fine now, and I'll miss my 6th sense, but the stir disc just wasn't viable in the long term. I do want to experiment with gaining this sense again, through non-invasive means - whether by embedding a magnet in a fake glue-on fingernail or by building a glove or ring to do it. But for now, I'll carry on as a normal, un-enhanced human.