We had a problem in an upstairs bath last year. The contractor put paper down our hardwood stairs and taped them with blue painters tape. When the paper came up, the varnish came up with it. We are now trying to get the house ready for sale later this year. Do I have to have the stairs refinished or can I lightly sand and revarnish? The stair beneath is fine and the varnish is off in spots. There are also places where the varnish is "loose". If I lightly sand, will that take care of that?

You will need to take off the loose areas.
It may take more than one coat of finish to make it look acceptable.
A random orbit sander used by a skillful operator will help.