There is a technique called salabrasion where the upper skin layers are rubbed off with a paste of salt. This doesn't remove the tattoo, but the ink is at least partially drawn up into the resulting scab during the healing process. It's probably not very safe, despite the use of salt, and removing skin like that over even a moderate area sounds brutal, but apparently it works well enough. And then, after one or more repetitions of the process, you are left with a highly visible scar, and maybe a faint tattoo, instead of just a tattoo.