Dic: blink (as a verb meaning: pretend not to see)

• a mayor who blinks at the corruption in city government.
• I just can't blink at that kind of behavior. 
• We can't blink at what evil you did.

* * *

■
  _2) (intr) to look with the eyes partially closed, as in strong sunlight
  _5) (when tr, usually foll by at) to be surprised or amazed: he blinked at the splendour of the ceremony
  _6) (when intr, foll by at) to pretend not to know or see (a fault, injustice, etc.)

■ 2. To pretend not to see. Also used with at:

• connive at, disregard, ignore, pass over, wink at.
• Idioms: be blind to, close (or shut) one's eyes to, look the other way, turn a blind eye to.

■ 6. To look with feigned ignorance: a mayor who blinks at the corruption in city government.

■ blink at something
  _ 1. Lit. to open and close the eyelids quickly, one or more times.

• I blinked at the bright light and finally had to close my eyes. 
• Don't blink at me while I am trying to take your picture.

  _ 2. Fig. to overlook something, such as a mistake. (As if one had blinked one's eyes rather than seeing the error.)

• I just can't blink at that kind of behavior. 
• We can't blink at what evil you did.

... Collins, Roget's II, The American Heritage, 

McGraw-Hill Dictionary of American Idioms and Phrasal Verbs