I think I would do as suggested and not mess with the backing.

The attached underlayment is going to be insignificant (1.2mm thick) in it's construction. Vinyl doesn't do well with underpad which is why the underpad on the plank is so thin.

Ignore the underpad. The flooring pro will be using a full spread adhesive when installing on the stairs. This itty bitty bit of underpad (it is pretty stiff all by itself...it's not the light and fluffy stuff on bad laminates) isn't going to cause an issue. Even if there was a micro-shift (so small you cannot detect it) the noising is going to keep everything in line anyways.

Besides, to shave down 1.2mm underpad, you will be sitting cross legged in your kitchen with a carrot peeler or a straight razor blade for HOURS and HOURS and HOURS. And at the end of your attempt you will have carved up your planks so badly as to make them unusable...thereby requiring you to glue down the regular planks anyway.

Thank you both!

And I agree - scraping it off sounded like a major pain!

Did you end up keeping the backing and just gluing down the vinyl plank? I see some people using brad nails as well. How is your stairs after 3 years? Please let me know. I m going to start this project next week!