If you wish to use polyurethane, strip all coatings off, sand it, then apply the polyurethane varnish according to instructions.
I prefer to use Tung Oil on my interior teak. Probably not a good idea to put Tung oil over a fresh coat of teak oil. Try it the next time if you choose not to use Poly.
On exterior wood, Starbrite teak finish lasts about a year in the Texas sun. Ordinary teak oil does not perform well much over 4 months.