A reman from a big box store is a reman, regardless of origin for the original unit. Get that unit re-checked at the store. It should indicate if it's a good unit or not. IIRC it can be done while still on the vehicle.

If it is bad, have them replace it with a good one.

Also if this happens in the future once they've replaced it with a good one, then I'd recommend finding a local shop that specializes in fixing them (via rewind, replacement of diodes, etc.). That's what I did and I no longer have these issues. <img src="/forums/images/graemlins/kewl.gif" alt="" />