If you give a bottle of breastmilk and baby only drinks some of it, do u have to throw out the remainder even if u put it in fridge right after?

I don't re-offer remaining milk for her next feed as I am fortunate enough to have adequate supply for my baby. I never ever pour away breastmilk. When she was still drinking expressed breastmilk from the bottle, whatever remained was stored in a Medela bottle for her milk bath each day. Now that she is direct latching, I use my frozen milk for her bath.