Can I trade-in my iPhone 14 Pro Max with green screen?

The phone has to be in good working condition. If it isn't that can, at best, reduce the trade-in value and and at worst, make it ineligible.

There's a button on this page at the top right that will help you figure it out:

Apple Trade In - Apple

If you can, take it to your local Apple Store and have them look at it and tell you.

All devices must be in good working condition to trade in, you can’t trade in a damage iPhone