My wife is following the religion well, but she has a question regarding her eyebrows. They are not straight and so it makes her look untidy and she feels embarrassed in front of people especially in Europe. People may think she is untidy and not clean and they will take a different idea about Islam specially that Islam wants us to be clean and tidy. Can she clean and remove what makes her untidy or not, as she only wants to be presented clean and not for beauty as she doesn't use make up when going out or anything except in front of me?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

What you mentioned in your question is not enough evidence for your wife to take from her eyebrows. It is unlawful for the woman to take from her eyebrows unless the eyebrows become a real disfigurement or deformation.
Your wife should be proud to be a Muslim and should stick to Islamic teachings to please Allah The Creator of the Worlds, The Only One who knows what is good for people and what is not. Allah Says (interpretation of meaning): {Should not He Who has created know? And He is the Most Kind and Courteous (to His slaves) All-Aware (of everything).}[67:14].
Allah knows best.