My old NAPA battery is toast, and is within its pro-rated warranty replcmnt period, so maybe would get $5-10 off if I swap batteries at a NAPA store.
If I want to buy a battery elsewhere for a better price (I do not have a costco membership, btw), how do I get NAPA to reimburse me for the pro-rated warr months?

If NAPA will let you, they will return the balance of the value of the battery, plus the core charge, if charged in your state. They may require you to buy a new battery at a discounted price instead. (I managed an auto parts store while going to college. Never heard of a 3rd way to handle it)

if you were not happy with their batteries in the first place, forget the $5-10 reimbursement and just buy a better battery somewhere else. I think these warranties are great if the battery fails just after 2 or 3 years (assuming it has a 2 year warranty), but then when you have only $5-10 of credit left, I think you already used the battery for 5 (maybe 6) years. Not worth the trouble IMHO. If you find a better price somewhere else, and more important, a better battery, just forger the small NAPA credit.

YMMV