The most common reason for scratches on the stainless steel handrails on a boat is the use of a hose that has not been cleaned when washing or rinsing off.
The hose, that may have been on the yard floor or pontoon, will have picked up grit; this grit along with the hose, scratches the stainless as it is pulled back and forth over the handrail.
To prevent this… clean the hose off before use, then place enough hose length on board for the wash. This way you will not be pulling the hose back and forth over the rails. Where the hose does meet the stainless, tie off with a cloth.
So, how do you remove the scratches?
Forget starting with metal polish, as it will only remove the very lightest of scratches. What you need is various grades of extra fine wet & dry sandpaper and some water, with a few drops of soap in to act as a lube.
Depending on the depth of the scratches (some may be just too deep) 600, 800, 1200 & 2500 would be a good selection. Follow with finer and finer grades until a reflection is formed.
Try with the finest you have to start with and only use a coarser grade if that fails to ‘flat’ them.
Example: if you have started with 1200, then use 2500 and finish off with polish or compound.
For deeper scratches, you may have started with 600, so then follow with 800, 1200 then 2500 and finish off with polish or a compound.