Ingrained means fixed so deeply that it cannot be removed. Ingrained habits, ingrained dirt, deeply ingrained.
It works for dirt in a floor and for attitudes in an institution, and the point in both is that surface treatment will not touch it. The grain in it is the fibre of wood or cloth, so ingrained means down in the fibre.
1adjectiveingrainedFixed so deeply that it cannot be removed.
“The habit of biting his nails was so ingrained that he did it without noticing.”
ingrained is a quality.
From ingrain + -ed.
Etymology from Wiktionary, CC BY-SA