"The woman is cleaning the car." Is not wrong! Cleaning up and cleaning are almost the same thing! Cleaning up usually means "picking up" as in, "The woman is cleaning up (or picking up) garbage." or "I am cleaning up my room." Cleaning is used in general. "I am cleaning my house." or "You did a good job cleaning." I am not a linguistics professional, but I'm a native speaker, and we say both and neither are wrong!

"The woman is cleaning up the car" and "the woman is cleaning the car" are the same and mean the same thing. Both are OK, but "cleaning" is more common.