Yes its normal. The Anti scuff is there just for protection, so as it sticks for so long, like aynthing when you try and take it off its gonna have a bit of give. Next time try using a hairdryer or somthing on it, will make it much easier.
When you took the scuff off, did you pull sideways or pull downwards? Cause you should always take it off across the grainsa nd not with them. If youve pulled it downwards it will affect the bat as you are pulling the grains off a bit, and ripping the wood. If your pulling it sideways it wont affect the bat even if little bits of wood have come off, it wont affect the middle, there really just surface tears.
To get rid of the sticky glue youll have to sand it down, and then oil it again (oiling it is essential). Youll have to wait 5 days after oiling it to then apply the new anti-scuff.