Nickel size dent in a stainles steel refrigerator door, how do i remove the dent safely and inexpensive?

if the dent is not creased; use a suctioncup dent puller availlible at any autoparts store

See this dent as character the price to repair is prohibitive however for cleaning I have the answer.
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It is more cost effective to replace panels than remove the dents. We can remove scratches but not dents, use DeBruce Polish for maintenance.

Find one of those auto body dent dent repair guys. They are the people that can pull the hail damage dents out of cars. Its worth a try.

going with the grain( s/s has grain just like wood product) try cleaning with a stainles steel cleanlingcloth and some wd40, this will remove any defect in th metal go with the grain not across you will leave rub marks if going avcross t he grain!!

Find and auto body that performes the paintless dent repair

dent pullers unlikely to work as door is foamed. you will be horrified at cost of a new door!

dent the other door to match

IF IT IS BRUSHED STAINLESS, AND THE SCRATCHES ARE REALLY BAD, YOU COULD TRY SOME STEEL WOOL TO SOFTEN THE SCRATCHES, BUT IT WILL BE A TRADE OFF OF MINIMIZING THE SCRATCHES AND CAUSING A SMEARED LOOK TO THE BRUSHED STAINLESS PATTERN.

you may some save $ by changing just the stainless skin outside the door. GE did on mine.

good luck