bat an eye|bat|bat an eyelash|eye|eyelash Идиома
bat an eye|bat|bat an eyelash|eye|eyelash
v. phr.,
informal To show surprise, fear, or interest; show your feelings.

Used in negative sentences.
When I told him the price of the car he never batted an eye. Bill told his story without batting an eyelash, although not a word of it was true. Compare: STRAIGHT FACE.
bat an eye|bat|bat an eyelash|eye|eyelash
v. phr.,
informal To appearance surprise, fear, or interest; appearance your feelings.

Used in abrogating sentences.
When I told him the amount of the car he never batted an eye. Bill told his adventure after batting an eyelash, although not a chat of it was true. Compare: STRAIGHT FACE. Dictionary