You can not remove the dye - -it will fade on its own through their lifetime as they shed their skin.

And yes, there is plenty you can do to help keep him healthy - - be diligent about keeping is environment clean - - read up on the Nitrogen cycle (ammonia/nitrite/nitrate) in the aquarium and how to cycle your filter (you are in what is call a "Fish-in cycle".
Make sure the tank is big enough - - this one frog should be in a minimum of a 10 gallon tank.
Maintain a healthy diet - - your young frog should be fed HBH frog and tadpole bites (found at petsmart and petco in the reptile section) and when he is over a year old you can start switching him over to ReptoMin Stick (also in the reptile section). The ReptoMin are floating compared to the sinking HBH and it will take him a bit to learn where to go for food but this is not anything to be concerned about. Do not feed feeder fish, freezedried cubed food, or an excessive amount of bloodworms.
Make sure the tank always has a secure lid - they are escape artists and can quickly die from dehydration.