I'll get it

* The doorbell rings and here's the context:

Grandpa: I'll get it.

Grandson: No. I'll get it. Stay.

Hello Native Speakers, does the sentence "No. I got it. Please stay" a much better and more polite alternative of "No. I'll get it. Stay" in this context? Because I think everyone should be civil to elderly people.

Thank you so much in advance