The story
Calque from Chinese 草書／草书 (cǎoshū), mistaking the character 草 (cǎo) as meaning grass, when in fact it refers to writing which is careless; sloppy; hasty, for example the meaning implied in the compound words 潦草 (liáocǎo) and 草率 (cǎoshuài).
Etymology from Wiktionary, CC BY-SA 4.0.