They tear off easily, leaving a tiny bit of residue. A quick hit on 320 grain sandpaper removes the last of it. Like quick quick, 5 or 6 strokes. If I had to do 100 of them, I’d cut a jig to hold them in place and then run a hand sanding block right over it.
You might be able to remove it with a solvent if you preferred, but I just went mechanical.
I have no idea what that backing is made of… I wouldn’t want to find out it was unsafe to laser. I’d be more likely to cut a jig for engraving as a gang. I just did the one, so I cut a 0.75" circle out of baltic and slotted the tile in for engraving. Can’t beat the accuracy of a good jig.
Just soaking them in water may take care of softening up the adhesive used to adhere them to the mesh so you can wipe/scrape it off the back (if you don’t have other reason to sand down the back).
I have too many horror stories of working with tiles on mesh that the mesh and even the adhesive used absorbed moisture out of the thin set/mortar bed & so had a mess to work with to get tiles relaid to finish bath or kitchen projects in various homes over the years!)