Salute with tears in one's eyes? (5)

I believe the answer is:

greet

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'salute' is the definition.
(I've seen this in other clues)

I don't understand how the rest of the clue works.

(Other definitions for greet that I've seen before include "Hail, salute" , "Say hello, hail" , "Welcome; cry (Scots)" , "Egret (anag.)" , "Acknowledge" .)

I've seen this clue in the Evening Standard.

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