The husband takes the top off the tube of toothpaste, and doesn't put it back on after cleaning his teeth. He takes a jar of pickles out of the fridge, unscrews the top and takes out a pickle. Then he puts the jar back in the fridge without putting the lid back on it. etc
He leaves the tops off everything.
You caught me. That is the correct grammar: 'leave the tops off of everything'.
'leave the tops of everything off' is stilted, and a native speaker would avoid it.
Because of how 'off of' sounds as you say it - like a stutter - and the similar position and movement of the jaw like a fish gulping water, in casual conversation you will hear (as I lapsed into) people say 'leave the top off the milk bottle', 'leave the tops off everything'.
Your grammar is going to be better than mine before long!