Many opinions, many experiences. There's a good possibility, depending on the damage, the strop can be used in a different way. If the surface can be rehabbed and smoothed a bit you could paste it and use it as a pasted strop. I've "recycled" several leather strops into linen strops. One can paste one side and add linen to the other side and have a brand new stropping tool. Bit of creativity increases the possibilities.