The part "먹다" in 귀먹다 or 귀가 먹다 is different from the usual 먹다, which is to eat, as you know.
Even native Korean speakers don't know what this means exactly, but the best explanation so far is 먹다 comes from the word '먹먹하다' or '막막하다' which means 'to be blocked' or 'to be fogged so that you can't see what's coming'
(앞이 막막하다 = The future seems foggy - you're worried about your future)
So 귀먹다 or 귀가 먹다 (not 귀를 먹다 because 먹다 here, again, is not the same transitive verb that means 'to eat' ^^) means your ears are blocked
But you'll notice that even a lot of Korean people don't know that this 먹다 is not the same 먹다, and would make the mistake of saying 귀 잡수시다 (잡수시다 is the utmost polite form of the verb 먹다) when they are referring to someone much much older.
But it should be 귀먹으시다 and not 귀 잡수시다
And FYI, someone who's deaf is called 귀머거리 in Korean.
And usually when two friends are quarrelling and one person yells at the other, the other person would say "나 귀 안 먹었어!" to mean "I'm not deaf!"
I hope this helps!
