What's the meaning of batting an eyelid?

[Bettyme]

English Idioms and Expressions, Advanced Level

ESL/EFL Test #3 "Lucky Alex", question 5

What happened was that the stupid animal took fright halfway through the course and without batting an eyelid decided to go back to the start.

(a) taking a chance
(b) turning round
(c) looking
(d) worrying at all

English Idioms and Expressions, Advanced Level

ESL/EFL Test #3 "Lucky Alex", answer 5

What happened was that the stupid animal took fright halfway through the course and without worrying at all decided to go back to the start.

Correct answer: (d) worrying at all
_________________________

what's the meaning of batting an eyelid? thanks.

[Mister Micawber]

Blinking
_________________
Native English teacher at Mister Micawber's

[Skim]

It means exactly what it was substituted with in the answer. "To [not] worry at all".

It means that you do something without fearing the consequences.