I’d keep the scourers away from your guitar. They’re for kitchen or the garage.
Buy some Finger Ease. Been around for over 50 years. About 10 bucks. Spray a bit on the neck, and polish with a cloth. Takes literally 10 seconds. I also spray a bit on my fretting fingers/ thumb too sometimes. The can lasts forever too, so cheap as chips.
Works a treat and won’t damage your guitar. I use it with my maple neck Tele all the time. Good stuff.
If you get some very fine 3M polishing paper 30 micron 400 grit and lightly sand the rear of the neck, that will do it.
You can also check out ‘Know Your Gear. com’ the guy knows what he is talking about and search for neck sanding, or something, there will be a video.