As long as I have been in this field, I have never been asked this question until recently -- and it has come up at least ten times in the past six months! Weird.
What do we do with this?
...I don't mean "will" will.
...He isn't really "right" right.
The first word is in the category of a word that is being used "as a word"; that is, we are focusing on the meaning of the word, on its definition. It is the same as
...What do you mean by "electrically"?
...When you say "tied up," what do you mean?
For this reason, the first use of the word is quoted.
Happy punctuating!
Margie