Post #788344 by nui 'umi 'umi on Thu, Jul 5, 2018 9:55 PM

Mike, maybe the Grackles are going after tiny insects on the limes as opposed to the limes themselves? I had a second look at your pic and it got me wondering.
Take a good look at the skins with a magnifying glass and see what you see. There are some good organic insecticides available including plain old soapy water in a spray bottle-you might not need that netting.