There are many aspects to this, in my opinion. The first being that yes, a country has it's own belief systems, culture and laws, which should be respected when traveling there. I have come across many examples of how what would be considered normal in western countries are entirely frowned upon or illegal in other countries, such as restrictions of clothing in some parts of the world.
Each country or peoples have their own rights to protect their culture, heritage and way of life, but i see no reason why the woman would have to be deported. She could simply be told to make sure that the tattoo was covered up while in the country and given a warning that if she did not, then she would face deportation. This is the way I would have handled the situation, however this is only my personal opinion. I'm sure the woman did not come into the country specifically with the intent of offending anyone, but she should have checked, the customs and laws of the country before travelling, especially whe traveling to a country so different in culture and law that the one she came from.