Patch of varnish rubbed away from pine table top?

We have a varnished pine kitchen table, and it got stained by a rotten potato that leaked from the bottom of a bag. Someone (naming no names...) then decided to scrub the stain away with a kitchen cloth. It's gone, but so is a patch of varnish about the size of my hand.

The wood underneath is slightly roughened, but I should be able to smooth it out with fine sandpaper and not leave any obvious holes or scratches. What I don't know of is a way to match the colour of the existing varnish. Do I have to plan for sanding down the whole tabletop and re-varnishing from scratch, and if so how many coats would it need?

This is in a rented house, the table belongs to the landlord, and we're moving out in two weeks. Just for added fun...