Try wiping with mineral spirits. If that doesn't work, lacquer thinner surely will. Open at least one window for this. Don't use paper towels or lint-emitting rags, it may stick to the surface. Next time let each coat cure before adding another. The minwax product is not 100% tung oil, it's adulterated to dry faster.
Casey

If you got pure tung oil to shine with just 3 coats, your coats were too thick. Pure tung oil requires the thinnest coats you can apply (rub on, wipe off everything you can after 15 minutes) with about 48 hours drying time between coats. This will take between 6 and 10 coats to get a shine.

Mineral spirits should dissolve the gummy tung oil. You don't have to get it all off. Let them dry for a few days. If it is still gummy repeat the mineral spirits. Once it stops being gummy, use the finish with which you are happy.

We used oure tung oil on our kitchen countertops. It is expensive, and sahron is right about the coating process. Instead of mineral spirits, you may be able to use a very fine abrasive pad to knock it down.
For your particular application (no food contact), I'd say go with the minwax stuff. If you're dead-set on pure, it needs to be rubbed in HARD with each coat.
I have a question on this same topic: we bought a gallon and it got cold one night and seperated. We haven't been able to recosntitute it.
It is white on the bottom and like honey on top. Any suggestions for salvaging this?

It's my experience with Minwax tung oil that you don't need a bunch of coats for a satisfactory finish. We used it on our clear fir trim, and did one coat, wiped after 15 minutes, and did a second coat and wipe 1-2 days later. Still looks good after many years.

Thanks everyone, this advice helped. Yes, Sharon, the coats were too think. The painter said to brush on a coat, let it dry, brush on another. This was not rubbed in. We are talking hundreds of square feet. Big job.

Great advice!