Word/phrase for taking offense but not showing it

Difficult. I might use chary or leery in some contexts, but not all, so this can only be a partial answer.

chary = discreetly cautious: such as

a: hesitant and vigilant about dangers and risks ”a government chary of getting involved in foreign entanglements”

b: slow to grant, accept, or expend ”a person very chary of compliments”

Merriam Webster

leery = if you are leery of someone, you do not trust them

Macmillan dictionary