Scrubbing is what you do with a brush and soap and water to remove hard dirt.
Scrubbing up is what surgeons do before going in to operate, i.e. cleaning their hands and arms.
Scrubbing up well is perhaps unkindly said of people who generally look a bit of a mess or poorly groomed and then make an effort, particularly for a special occasion.
Britney can really scrub up well when she makes a bit of an effort. There’s a real beauty hidden beneath those shapeless grubby jeans she loves to wear.
Jon scrubs up well if he’s going out on a date.