I use lemon oil on all my teak furniture, it makes a huge difference! Just rub it on liberally, let it soak in for an hour or so, and then take a clean cotton cloth to rub off any excess. You might want to do it twice in a two week time span, then it only needs to be done once a year or so. I would give that a shot first before trying any light sanding. remember, most of the teak flat surfaces are veneered and most were finished with an oll finish, not a varnish or stain.
I refinished our Danish Modern teak dining table and chairs, which dated to the 50's and were badly scratched. I cleaned the wood thoroughly with Formby's, sanded the table top and the arms of the chairs with medium and then with fine sandpaper, using a hand electric sander, and finally rubbed in several coats of Formby's tung oil . The set is beautiful, like new again. These pieces are solid teak, not veneered - the tabletop must be 1 1/2" thick. The chairs have had the wool upholstery very carefully taken loose, the original sagging rubber webbing replaced with new rubber webbing - expensive but worth it - and the padding and upholstery put back. The wool upholstery is wonderful, I clean it with Woolite upholstery foam after Thanksgiving, when the grandkids drop food on it. I love Danish modern - if you buy quality you'll keep it forever.