Hello!

Thanks for writing in. This is common in the Spring, and the squirrels should move on soon.

Squirrels usually chew bark looking for sugar or nutrients. They also chew to get some of the sap, which hydrates them and provides them some carbohydrates. Extensive chewing can cause some dieback. If it's less than 1/4 of the way around, the branch is likely to survive. If it's more than that, it can cause damage to the tree. Only time will tell. 

Options include exclusion (if possible), motion-detector sprinklers, or wrapping the trunk or the chewed limbs in metal (like a cage). Around the trunk, sheet metal works best. This works best, of course, in situations where the squirrel cannot jump to the tree from the roof, fence, or another tree.

There is not a way to repair the damage, only to prevent in the future. Next Spring I would keep an eye out and wrap the tree with metal if possible. Hopefully the tree will be ok, trees are actually quite resilient.