Should I remove padding on laminate flooring before gluing it to steps?

I have some laminate flooring that I’m installing on a few steps that lead into my sunk-floor family room.

The flooring is intended for a floating installing, but I know that on steps I have to glue and nail it to keep it stable.

The manufacturer appears to say nothing about stair installation. I read through the warranty/install guide and it only address the floor installation. It excludes certain things (i.e. ceilings), but doesn’t exclude stairs. Here is the product page.

The flooring I bought comes with an attached pad. Do I have to remove that before installing?

If I don’t remove it, I’m concerned that the bond won’t be a strong as needed, or that the padding will allow shifting.

If I do remove it, I’m concerned that it will make it a slightly different height than the stair nosing.