Ethical behavior generally requires honesty and forthrightness. If you are only concerned about your own ethical behavior, you should tell them. Keeping it a secret is effectively lying.
Why? Virtually all companies keep secrets both from their employees as well as their clients. In fact, these are even protected by force of law. Why is it dishonest for the employee to act towards the company in the same way? Isn't that a double standard?
I addressed this pretty directly in my second paragraph. Some people are interested in behaving ethically even in the face of unethical behavior. It is absolutely a double standard, but one that a person willingly applies to themselves.
No, it's not a matter of "they're unethical, so I can be too"; I don't see why keeping a secret is necessarily unethical in the first place. Are trade secrets unethical?
Keeping a secret is not necessarily unethical, deception is (with the same caveats as above). For instance, your employer isn't ethically obligated to tell you how much money your co-workers make. However, if they do tell you, they are ethically obligated to tell you the truth.
In this case, the author has told the employer that they are doing this work in a certain way. They are continuing to lie about it in ongoing way by intentionally including mistakes to make it look as if they did it by hand. This is unethical deception.
If the author truly believed that the employer didn't care, then keeping it a secret would not be unethical. But clearly this is not the case.
Why? Virtually all companies keep secrets both from their employees as well as their clients. In fact, these are even protected by force of law. Why is it dishonest for the employee to act towards the company in the same way? Isn't that a double standard?