Since it was asked, I decided to take it upon myself to delve the depths of the delicious delicacy.
Alteration of Middle English grutta, coarse meal, from Old English grytta, pl. of grytt.
I’ve recently discovered McCann’s Irish Oatmeal and it reminds me of grits in it’s way, so the Old English to the Old South connection doesn’t seem as far of a stretch to me as it once would have.
Welcome to wordorigins, johnsy.