There's an English paper saying "blink at = show surprise", and "blink at" is a phrasal verb. I've searched a lot of places and didn't see any saying the same thing. Is this true? Does anyone know? Please let me know, thank you.
Yes. A phrasal verb is made up of two or more words (ThoughtCo). Phrasal verbs attain a meaning that is distinct from taking the literal meaning of each word and combining them. For example:
I turn on the TV
Turn on is a phrasal verb meaning to activate. It has its own dictionary entry (Merriam-Webster). It doesn't mean literally to turn | on the TV, as if one is turning relative to the TV. In a sense, phrasal verbs often form from transferred or figurative senses of verb and particle or verb and preposition combinations.
In the case of blink at, it can qualify as a phrasal verb. As a phrasal verb, according to Lexico, it means:
(blink at) [usually with negative] React to (something) with surprise or disapproval.
‘he doesn't blink at the unsavoury aspects of his subject’
In this context, blink at has lost the literal sense of blinking in the direction of someone. If I said,
I blinked at you, but you didn't notice.
That's not a phrasal verb, but a verb and a prepositional phrase describing direction. I literally shut and opened by eyes. Where? In your direction. Similarly, "I didn't blink at you" would describe me not shutting my eyes. Where? At you. However, if I said,
I don't even blink at my colleagues' behavior anymore. Nothing could surprise me.
That's a phrasal verb, because blinked at together conveys a meaning idiomatic and distinct from the two words separately. I am not surprised. The state of literally blinking is irrelevant to the meaning, except in a residual or figurative sense that people who blink are surprised; I don't blink; therefore I'm not surprised. The usage is habitual enough that the logic chain doesn't need to be invoked to understand the usage, just like one does not need to logic out other phrasal verbs. Someone reading this as an admission of not shutting their eyes would be in error.