Look at the pic below. In a nose dive crash onto asphalt yesterday, this battery took a beating as you can see. No sure exactly how it happened but should I still use it or get rid of it? It’s. It’s not puffy and it appears as though only the plastic wrap was torn but idk if it’s safe or not....
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It might very well be ok; I've got a couple of batteries that have been a little beat up from quad crashes where the plastic wrap on it has come off.
That said, there's still a good chance that there's some damage you can't see. Have you tested the battery to see if there's any internal resistance on a particular cell, or if there's any wild variation of charge between the cells (i.e., cell 1 and 3 show at 4.17v, but cell 2 shows at 3.8)? That could indicate damage that's not visible.
If nothing seems to be the problem, then you can just throw a little electrical tape around the wrapper and continue to fly it - but I'd recommend charging it in a Lipo bag or something with some fire resistance, and monitoring it during the charge, to make sure it doesn't start puffing up, just in case.