Hi-Low table refinishing

Our 71 Egg Harbor came with a nice little Hi-Low table that folds out. The current finish on it is pealing off. Is this something that you varnish? Or just teak oil and a lot of it?

I would like to re-finish the step ladders and the deck door trims to all match the table in the end.

For a table that's kept inside, the finish is likely not taking a lot of abuse. So you can finish it with whatever you think looks best or provides the best surface.

Personally, I've got a teak hi-low table that's oiled (like the rest of my interior teak). And a hard mounted table on the bridge deck that's cheap wood with veneer over it, but was coated with polyurethane to keep the veneer from fading further. And that had the bonus of making the table much more grippy when placing things on it. As in, a plate of food will generally stay under reasonable conditions instead of requiring a grippy mat placed under it to prevent sliding like the other surfaces of the same material.