From Longman Dictionary of Contemporary Englishblink back/away tearsblink back/away tearsto shut and open your eyes in order to get rid of tears Lynn laughed, blinking back unexpected tears. → blink
Examples from the Corpus
blink back/away tears• I noticed that his hands were trembling slightly, and he seemed to be blinking back tears.• She needed to blink away tears.• Touching the welt, Howard tried to blink back tears before going inside. 