I added Bell Hammer 7 to the engine oil (50 ml) and final gear oil (5 ml) of my Honda Tact scooter. Later someone said “it’s chlorine-based, so it’s bad for the engine.” Is this harmful?

Bell Hammer 7 contains a very small amount (0.4% or less) of MCCP, formulated to meet international environmental and safety standards. It does not cause corrosion, nor does it damage common seal materials such as NBR, FKM, or silicone rubber.
The Honda Tact uses a CVT without a wet clutch, so there is no risk of clutch slippage.
The amounts you added (50ml engine / 5ml gear) are within a normal additive range, and you can continue to use the scooter without draining or flushing the oil.
You should simply proceed with your next oil change at the normal interval. The product will help reduce wear and noise, and no special action is required.