Brillo Pads or any other abrasive cleaning pads will scratch the stainless steel surface so you should not use Brillo Pads or other abrasive cleaners for stainless steel because it will damage the finish of the stainless steel.
You can use regular dish soap or non abrasive cleaning solutions and use a sponge or just use a washcloth to clean the stainless gently.
You can also use some Clorox Cleaning Wipes to gently wipe down the stainless steel which will help the stainless steel shine as well as help disinfect the stainless steel.
As long as you use something gentle and non abrasive to clean the stainless steel then you should be fine without damaging the stainless steel.