I usually remove the chicken wire after a few weeks once the ground has settled and the squirrels forget where they are planted.

Go ahead and pull it off anytime. You may want to wait if you have buds so that you don't break off the buds.

Another thought. Do you feed the squirrels? I set out all kinds of extra food scraps that they and other critters consume and I don't think I get that much digging. But if I put something in a planter on the fence that is their raceway, they will dig in it so I keep one there with useless to me items and let them dig away. Of course with a big garden and a big yard this might not work.

I wouldn't dare feed the squirrels here, we have so many. We do have two oaks so they seem to be well fed and usually don't consume many bulbs.