Is it permissible to claim monthly travel outside the city in order to receive financial compensation, knowing that the travel is internal and everyone is aware of that, until the problem of the company not paying compensation for internal travel is resolved?

If you are entitled to a transportation allowance within the city and find no way to obtain it except by claiming to have traveled outside of it, there is no blame in that. This is because lying is permissible if it is a means to obtain a right, provided that you do not take more than what you are entitled to.