I have never had squirrels or chipmunks dig up my garlic...but maybe I have been lucky?? Last year I did cover my garlic with a mesh screen, but took it up before the snow fell, as I was thinking about how early the garlic starts to sprout and I did not want the cover to stop it....I did not plant mine yet this year...but have had squirrels digging up my freshly transplanted iris's...
good luck with the garlic, it is wonderful to grow your own, I love how they grow and the scapes are great in early summer.. martha/zucchini