How do you get rid of the musty smell in the heat pump. It is only there when the air conditioning is on.

I don't think the smell is the heat pump. Otherwise you would smell it when the heat is on. I believe you need to have the evaporator coils cleaned. The coils are always wet when the AC runs and in the summer, hot humid air allows mold and mildew to build up. The water you see dripping outside or in your condensate pump comes from the coils. This is not typically a DIY job since the top front of the air handler must be removed.

Get a qualified person to inspect and probably clean your system. It should be done BEFORE you turn on your AC for the cooling season. This does include vents and ducts throughout your home. When was the last time you did this routine preventive maintenance?