Sand it down, then restain/refinish.

I agree that it should be stripped and then sanded. It probably does not have a catalyzed finish so it should be too difficult. If you are stripping it in the house use a non toxic stripper such as the non toxic version of Peal Away. It is a paste that you apply and let it sit for 24 hours. Then scrape with a sharp scraper being careful not to dig into the wood holding your scraper level. Then start with 60 grit paper and finish with a 220 grit or 400 grit. Make sure all the finish is removed. Test with alcohol to make sure the finish is all off. You can use a high speed orbital sander on the top but keep your sander level and don't dig in with the sander.

I might suggest leaving the finish natural with no stain. Then finish with two coats of marine Varnish and two coats of satin varnish and use a product call "Fine Paints of Europe". You may have to buy it online. The company is from Europe but headquarters is in Vermont. It can be applied with a brush and is superior to any other product I have used. It goes on easily. Doesn't have much odor and will look like a factory finish. It is about $30 a quart and you will have to buy a quart of each marine and satin.