A good way to get burn marks off a stainless steel stove top is to spray some Easy Off oven cleaner or any other oven cleaner onto the burn mark.
Allow the oven cleaner to sit for a few minutes and then use a scrub brush to help scrub the burn mark off the stainless steel.
You can also pour some boiling water and some baking soda onto the burn mark and allow it to sit for awhile and then use a sponge or the scrub brush to clean off the burn mark.
Club Soda and and baking soda is also another good cleaning solution for cleaning burn marks off of stainless steel stove tops as well.