The Chinese characters in Matthew Fox's real tattoos mean "Eagles cleave the air", and the producers did not actually cover up these characters with new ones that mean "He walks among us, but he is not one of us."
The tattoo that Jack gets in Thailand is actually a real tattoo on actor Matthew Fox. It is covered with make-up before he receives it in the flashback scenes, but this is obvious as the color doesn't quite match his skin tone.