When it comes to 粗, Henshall says 米 means “rice.” No surprise there. Meanwhile, 且 is “furthermore,” acting phonetically here to express “neglect” and almost certainly lending connotations of “to accumulate.”
Back in the day, one accumulated rice in a storehouse. Indeed, 粗 originally referred to spilled rice left neglected in a corner of a storehouse. This kanji later acquired the broader meaning of “poor quality, coarse, rough.”