How to remove scratches on varnished wooden door?

There are several finish repair products on the market. You can get most of them from the usual getting spots.

I've had very positive results with "restor a finish", they sell it in multiple colors so you just need to find the one that most closely matches the wood you are working with. There are also "fill sticks" that are probably better suited to deeper scratches. Also "Feed-N-Wax" will make a lot of scratches less visible.