Another member here, Bert, turned me onto Run N Buff and I've had good results on tiles. I'll add something to Kev's mention of WD40, it will also remove Rub N Buff. I originally tried WD40 to clean the excess off tiles but once it got in the engraved ares it caused some of the run to flake off. I found if I flip the tile over, engraved side down, onto a flat rag with some alcohol the excess comes off and it doesn't interfere with the engraving. But WD40 will get it off anything you accidentally or purposefully get it on.
As for Cermark LMC-6044 I've had mixed results with it. I managed to get it to stick to some Lowes tiles but the same settings didn't work on HD's similar tiles. They looked good but the second I rubbed them in the kitchen sink it wiped off. I called Cermark tech support and they basically explained that different materials (tiles, metal, glass, etc) can vary and require testing. The guy I talked to said it's supposed to melt to the surface more than burn so I think running test grids is best way to find your settings. It seems to melt better with a little dwell time (running a medium speed) that way you're not running so fast that you ablate it or barely heat the surface.
RayFine Fiber Laser (JPT M6+, Sino Galvo head)
RayFine RF-1390 100w EFR
Blast Cabinet, Vinyl Cutter, Sublimation Equipment, CNC