Damaged backer board during shower tiler removal, repairable?
No, I would not consider trying to repair that. Nothing you do will restore its integrity all that well. Thinset would be a band-aid fix though. Fact is, there are two other major issues with your shower than will contribute to its eventual demise.
First, the installer used mastic. Mastic should never be used in wet areas...Thinset is what's needed.
Second, the backerboard doesn't have a waterproofing agent applied to it. That's ok if you have a vapor barrier between the wonderboard and the studs, which you might. Grout and backerboard are incredibly permeable, and water that infiltrates the grout must be confined to the backerboard (to protect the studs from rot and the wall from mold) or prevented from getting in it in the first place.