What is this glue layer on top of the slate stone flooring?
The mesh was a heat activated glue strip to join carpet usually found at doorways and if the room was wider than the roll 2 pieces are butted together and a iron that heats the glue and carpet is used to melt the glue and make a seam. Some of the heated glue sticks to the floor but it is used for the splice. Most places use 4" wide but I prefer 6" as it holds better.  This stuff releases with heat a heat gun is what I use but a hair dryer on high heat low air flow may be hot enough. A razor scraper will shave and left over glue, and a bit of heat makes it softer (think hot glue gun) for the type of glue used.