Usually these kind of tables were made with an oil finish but you may find some with lacquer. You can test for lacquer by dipping a Qtip in nail polish remover and rubbing the a glossy area of the finish. If it's lacquer, it will dissolve very quickly and the gloss will be gone.
If it's an oil finish, you can start by cleaning and oiling it. A lot of very dull, dry teak will look beautiful with just one application of oil. Some will take a bit more work. Use teak oil with #0000 steel wool and always have the steel wool soaked in oil, don't rub it on the wood dry. The oil breaks down the oil oil finish and any dirt that's on there. Let that sit for a few minutes, then wipe off. You can repeat it the next day if you want.
And yes, it's veneer. One of the fastest ways to wreck veneer is to sand through it, so if you don't have to sand, don't! I think chemical strippers are ok on it if you have to strip varnish or paint off, but most of the time you don't have to be that drastic.
Oil is a very forgiving finish.
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