Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
This bandage on your wife’s arm to prevent water reaching the skin, because the water harms her, has the ruling of splint (plaster).
We wipe over the splint either when making Wudu or making Ghusl. Therefore, if your wife has to make Ghusl, then she has to wipe over this splint and wash all her body. By doing so, she becomes completely pure. But the splint should not exceed what is needed. If she needs to cover just a part of her arm, then it is not permissible to cover the entire arm.
Allah knows best.