I got a new clothes washer yesterday (sweet!) and on taking the old
one out, found one of the leveling legs had rusted and left a very
noticeable stain on the tile. The tile is a matte finish, generally
cleans up pretty well. I've tried a couple of so-called rust remover
products (nothing specific to tile), which have helped, but there's
still a distinct round, rusty circle on my off-white tile (don't get
me started on keeping off-white tile clean in general in a utility
room, don't know what the previous owners were thinking). The new
washer has a different footprint from the old one, so the stain is
right out there to be seen.

Any advice?

Jo Ann