I use Clorox Bleach tablets with great success. You just put one in the tank--each one lasts for 1-2 months. When it's gone, plop another one in.

Usually bleach is not recommended for the inside of the tank. Bad for the rubber and plastic components. That being said, check with Toto and see if they allow it.

I was afraid of damaging the plastic and rubber parts, I think I will contact Toto and ask them. Thanks.

I wouldn't do this. I remember Toto giving me free replacement flappers early on but claiming that chloramine in the water would cause the rubber to disintegrate (we only have chlorine and no chloramine in our drinking water). What you're talking about is maybe 10X or more chlorine all the time than is in the water as a disinfectant.

Also, make sure your nose isn't deceived by a smell that isn't really coming from the toilet tank.

Use bleach (10% final concentration). Treat for 10 minutes only and brush the solution up the sides and onto the inside of the lid. Flush the tank sides and inside the lid well after treatment. 10 minutes will kill fungus and limit exposure of the metal and soft parts. Hypochlorite corrodes metals and oxidized organic polymers so I recommend against constant exposure.

Thank you for your comments.

I feel that we can use the Clorox into the tank for less than 10 min. and flush it in-order to stay in the toilet bowl for to remove any marks that often stay even after the cleaning.

If you replaced the toilet already because the old one smelled musty, and the new one now smells musty, too, why do you think it is the toilet that is musty smelling? I would bet it is the floor or the wall that is musty. You probably have had or still have a slow drip or condensation drips that are keeping the floor wet or the studs in the wall wet. Since this is an outside wall, I think this is even more likely.