not bat an eyelid (or eye) show no emotional or other reaction. informal

☞ Bat in this sense is perhaps a dialect and US variant of the verb bate meaning 'lower or let down'. The variant not blink an eye is also found.

2012BenSilent Words Speak Loudest When a man wearing nothing but socks and a hat walks on stage … Kay does not bat an eyelid, simply dropping his trousers and carrying on with the song.