I would suggest stripping all the old varnish of with nitromorse varnish remover,make sure you use gloves as it burns , to get the really stubborn marks out only use medium course steel wool or medium grade sandpaper so as not to mark the old wood not forgetting to only rub down in the direction of the wood,not against the grain of the wood as it will show when you re apply.
I would suggest either using a teak oil or a clear varnish to re coat, one or the other NOT BOTH,the oil would be the best thing for the wood as it still lets it breath and brings out more of the old woods natural beauty.
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