Hey. I can't see the image at the moment so I'm not sure how severe the damage is.
As long as they are okay, no risk of infection and the axolotl is happy enough and eating the only difference I'd think it would make is your axolotl may go for air more often.
Whether or not they will grow back is another matter. I've got one axolotl whose gills I presume began to shrink due to quality of life and his haven't grown back much just yet, and possibly never will.
But another whose gills were nipped off now has bigger gills than when he first came home, but not as big as my axolotls who have never had gill problems.