Do I need to get the protective screen on top removed before trade in?

I would use a credit card and remove it so you can see if the screen itself or the frame has been damaged. Also, just prior to sending it in take good pictures of the phone form all angles and a short video of the phone actually working.

The evaluation will be of the device itself, not any protectors. If the current protector can be removed, it should. It shouldn't matter what condition the protector is in. For example, I have traded in a number of my iOS devices over the years. Most, if not all of them, had some type of protector when I used them. For me, all of them were easy to remove and I done so before sending them in for the evaluation.

If you have not used the Apple Trade-in process before, it is quite simple:

• You fill out a short online questionnaire to the condition of the device answering the questions as honestly as possible. You will then be provided with an estimated trade-in value for the device.
• You will receive a pre-paid shipping container to send the device to the third-party evaluator outfit.
• Typically, it takes a week or two once they receive it, to complete the evaluation. The results are either they agree with your evaluation or they will inform you that they don't. For the latter, that will result in a lower trade-in value than what you were quoted online. You will then be offered a choice between accepting their reduced offer amount or having them ship the device back to you at no cost.
• If you accept the evaluation value, then depending on what option you choose when ordering your new device, is how you will receive the actual amount.

No, it shouldn't be required for the trade-in process. The third-party that Apple uses to verify the condition of the phone will, most likely, do this for you in order to properly evaluate it. However, if possible, you should remove it before you send it in.