Did I err in covering the picture of an unveiled woman on a postage stamp for my brother, and was my brother justified in his anger, believing that it was not within my authority?

The sight of a woman who is immodestly adorned is a reprehensible act (munkar) that must be changed by hand for whoever is able, provided it does not lead to a greater tribulation. What you did in changing this reprehensible act is permissible, and your brother's objection to it is not valid. You are thanked for your action.