If its several 1 inch or so small areas, I would localize my repairs to the spots. I would steel wool, stain and re-poly just the localized spots. If you do a good job nobody will notice. If you do a decent job, then you will be the only one to notice.
I wouldn't do the entire floor. You don't strip poly, it is sanded off, but if it is chipped away in small spots then there is no need to remove. Stain penetrates into wood you cannot strip stain. You may need to reapply stain to match the color of the surrounding areas. Talk to a local stain-woodworking professional at a hardware store (if any still exist) and get advice about matching stain. I forget if the color of stain gets lighter or darker after the coat of poly is applied. Finally re-apply poly to the small areas of repair, use a foam brush and feather in a small amount of overlap. Make sure to use same type of poly gloss, semi-gloss, or satin in order to match the finish.
When you are all finished, if you are unpleased with the result, then you can spend $3.00 per square foot to have the entire floor redone by a professional.