It appeared on my Note 5 recently and I, too, could not get past it - at first. I did discover a workaround which suggests an app flaw or exploited bug:
- Turn on Airplane mode
- Start the Internet app - it will stop with an error about no connection, but it will not display the adware message
- Click More, and find Settings
- Select Homepage and choose Other web page
- Enter your preferred home page URL (e.g.: Google), [notice that the "Current Page" option shows the URL to the bad adware site]
- Click the back arrow until you get back to the browser main screen.
- Turn Airplane mode OFF, and try going to the home page. It should work, and the "Current web page" should also say whatever you entered in the "Other" entry, since that's where you last were.
You can also go and set the "Home Page" URL to the same preferred location.
The point is that this Samsung Internet app might have a bug or exploitable flaw that continuously uses the "Current Page" URL, even if it is not selected.
I'm guessing that at some time while using this browser, I must've hit a site with popups or a poisoned ad, and since that was the last [current] page, it stuck.
In the meantime, I'm sticking with my Chrome or Firefox browsers - this built-in Samsung one is bogus...
I'll also yell at Samsung, to describe my adventures, to see if they know about it.
FYI, I wiped system cache ("three-finger-salute" startup to android menu option), force-stopped the Internet app, checked for updates, scanned with Malware Bytes and the Verizon protection tools, and spent an hour on the phone with Verizon. Whilst reviewing and redoing everything that I had already done, I stumbled across the idea of using Airplane mode while starting the app, to finally get into its settings. I hope you find this useful. And if you've found other solutions, that would be nice to know.
Ciao for now...