What does pay out the proceeds mean on form 1310?

Replace the word "proceeds" with the word "refund" and see if that helps you comprehend it easier.

if you are the person entitled to receive and keep the refund, the answer is no.  if an exceutor, trustee or someone  else signing the return but who  is not entitled to keep the refund the answer is yes unless you keep the refund you're not entitled to.