Stripping teak. What to use?

Like Ralph suggests, a light sanding then overcoat. If you sand through to bare wood, there will be a color difference, so consider how much it offends you when coated, because the only option is to get everything back to bare wood. Having a slightly darker "birthmark" in the finish is something most people don't notice, but can drive you crazy if you're that type of person. I'm more forgiving when looking at a project like that. I used to obsess over perfect and dust-free coats, until I learned that varnish surfaces can be wet-sanded and polished like any plastic. Sanding between coats removes too much applied material, so I scuff with a brown 3M Scotchbrite pad between cured coats. It's also possible to lay on "hot coats" relying only on chemical adhesion if the preceding coat is "green" and the weather is right.
An inexpensive way to preview what it will look like, you can Scotchbrite the whole thing, solvent-wash with paint thinner, and rattle-can with something like THIS. Cheapest way to get started with varnish, since the good stuff is $80+ for a quart. Sacrilege, I know. I've been down the Epifanes and Badger brush path, but ultimately, all varnish is temporary and requires maintenance.
If you want to keep that lovely honey-gold appearance, I would suggest Schooner Gold, especially since it builds faster, too.

You're going to have to strip it. All of the areas that are white will show through if you don't. Take it to Bluewater chairs and just pay them to do it.

Stripping and light sanding, then 12 coats of Epifanes would be best, but lots of work..
I agree with the poster above: Do NOT sand between coats, just use a scratch pad.
As a previous owner of a wooden boat in the tropics and another boat with lots of external teak in SE Florida I have been down that road many, many times.
I never got really good with a varnish brush, average at the best, but I hired experts to do the deed on my behalf

I had Mr. Greene on the payroll pretty much year around since 2007 until 2016.
We had a thread about him right here on the YachtForums.
In a nutshell: The Epifanes would last 12 months in the Fort Lauderdale sun and every May Mr. Greene would sand off the top UV damaged layer and build up 5 new coats, and they would last another 12 months.
This was After I had him strip all external varnish of my 33’ sailboat and built up 12 new coats as the base coats, then every year 5 new coats, etc.
He also did the interior but since the sun doesn’t shine down there it was just light sanding and 2 coats after 30 years.
Needless to say I funded Mr. Greene’s retirement and a lot of donations to his church.
(He was a very religious island guy from Nevis and always broke because he gave away the money to some priests who most likely spent it in Las Vegas)

At any rate, your small project can be done either way, strip, sand and build up with new coats, or just sand lightly and blend in new coats hoping it will look like the seat back has a personality and a “patina”.
This would be a fun little winter project if you have the time, or hire a pro to get it done in a week or two.
The below picture is Mr. Greene’s work

Look for a new one for 1/2 the price..?

It can be stripped in 1 day, then gentle sanding before building up half a dozen coats, should be $5-600 in labor max, plus $50 materials.