DIAGNOSIS You have grease or oil transfer from the washer's internal mechanical components, most commonly from an over-lubricated or failing transmission shaft seal.
FIX Run an empty cleaning cycle immediately. Use either a washing machine cleaner packet or two cups of bleach on the Clean Washer cycle with hot water. This can dissolve and flush away some surface grease.
IF THAT DIDN'T WORK The transmission seal may be actively leaking. This is a significant repair. Check for oil residue inside the tub near the agitator base when the washer is empty and dry.
HEADS UP Wash the affected clothes again with a heavy-duty detergent and avoid drying them until the stains are gone, as heat can set the grease stain permanently.