I was told not to use oil because the wood can't breathe and then you can get mildew in damp locations. I am still waiting to get all my chairs, so I haven't treated yet, but I was told to use a water based protector. The one I got is linked below, but I'm sure there are many different sellers with similar products. I would call one or two of them and ask if the cleaner will be enough to remove the oil and clean the wood and how they would reclaim and protect the wood. Good luck.

Here is a link that might be useful: Teak protection kit