It looks like you are in a career-defining situation, where you have to decide whether you are going to do as ordered when you know it is dishonest.
Once when I was young, I worked in a business where I was told to tell a client something that wasn't true. I did as I was asked, got very little sleep that night, then quit the job the next day, and called the client and told him what I had done. (Needless to say, I was persona non grata at my previous employer's after that.) Nowadays, I would have worked with management to look for an honest solution to the problem, and would have quit the job if I couldn't convince them to change their proposed solution. If honesty is important to you, you can always find people to work with who it's important to as well. Dishonesty becomes a habit, and a heavy burden to bear.
If you do decide to go through with it, I hope you raised your concerns and got your response in writing, so they can't try to blame you for it if things go sideways. If you didn't, then try to get things down in writing; find more reasons for concern to have a reason to email, and email them to your management. If you find down the line that you have behaved dishonestly, please keep in mind that honest people are not people who are never dishonest, but people who own up to it when they are, and do their best not to be dishonest in quite the same way again. Everybody is dishonest sometimes in one way or another, especially with themselves.
By the way, when you are working with dishonest management, "reflects poorly on the company" isn't typically something that they much care about. It might be more persuasive if you explain the kind of trouble they can get in if they violate the TOS of the company (especially if it's a big company) who provides the content you describe.