This reply is meant for the benefit of future readers, because i guess OP is long gone by now...
Anyhow, HCl, which is the acid present in Muriatic acid, should never be used to clean any steel. Chlorine will remain on the surface and accelerate corrosion.
Stainless steel seems to not rust, because it is passivated.
An acid like nitric acid or citric acid is used to selectively dissolve iron from the surface increasing percentage of chromium from ~11%, as found in bulk stainless steel, to a much higher amount at the surface. The exposure to air and moisture causes chromium to oxidize, forming chromium oxide layer. Unlike rust, chromium oxide layer is much stronger than iron oxide hence it stays on the surface and protects against further rusting. Eventually, wear and tear will degrade the chromium oxide layer exposing fresh iron atoms and rust will form. Repassivation can fix the issue.
For a home DIYer the citric acid is the best bet since nitric acid can be a rather nasty chemical to deal with.