The Min Nan "t" is an unaspirated consonant (meaning if you hold your hand in front of your mouth when you pronounce it, you shouldn't feel the puff of air), like the t in Spanish. English speakers routinely interpret these sounds as aspirated consonants since we lack those sounds. Why Dutch writes it as thee, I don't know, since Dutch lacks aspiration. Wiktionary just said the h is faux-Greek but I don't understand the motivation of that.