I was outside watering. We are supposed to get up to 80F today .
I don't know that I have ever seen a pest/insect on a piece of cork. But, that being said, I put my cork in a large tub of water and weight it down so that it stays submerged for an hour or more. I do this simply to dissolve any salts/debris that may be there. If you have pests, they won't remain under water and will float to the surface where you can remove them. I guess flooding the cork with an insecticide would work. I just don't used pesticides on my slabs.
I have a little concern about the dark coloration of the inner surface though. Here are a few examples of what I have and notice the light tan color of that inside surface (and all the lichen/moss on the outside surface). Even cork that I have had mounted for years still has that light tan color. I don't know what your dark surfaces represent. Does that surface smell smoky? Perhaps it was treated with some sort of ferrous solution?
I always mount my plants on the outside surface since that surface presents lots more undulations/coarseness, giving those roots more opportunity to "grab hold".