I don't think there is a correct answer to your question.
But I think you should show your work to a friend (who has more experience with the deprecated way of doing things) before you send it back to them.
And no, I'm not even suggesting that you be deceitful about it. Once you're in front of the right person, you can tell that person what you did.
"Hey, I know this new api like the back of my hand, but since I have less experience with the older api, I had a friend look over my work (just in case)."
In other words, by saying this, you show them that you're an expert in the new stuff, but you still show your willingness to work with the old stuff. And honestly, any hiring manager worth their salt will know that if you've mastered a new api, that you won't have any trouble mastering an older one (assuming you're enthusiastic enough to do so).