Does backfiring in a decelerating motorcycle engine cause damage to the engine?

Answer

No it doesn't cause any damage your just running the bike too rich you should try to use a higher octane fuel and that should balance it out. However, there is another possibility and that is the bit of rubber "hose" connecting the carburetors and the inlet manifold / cylinder head has deteriorated. The rubber becomes hardened as it ages, and air leaks can happen. This means that the mixture of gas and oxygen that gets to the engine has too much oxygen in proportion to gasoline. The only way to fix this is to change the rubber parts. These may be easy or difficult to obtain, depending on the age and or make of the motorcycle. I read somewhere that increased oxygen makes the engine run hotter than normal, under these circumstances, when the short rubber hoses get hardened.