Karen, what brand of SS scrubbies are you using?
Are you scrubbing under constant stream of running water, OR in a sinkful of standing water?
If you still have 'reddish' residue washing off, the piece is not properly derusted.
The converted rust will be black, that is the color you want to see rinsing off.
I have noticed a definite 'cheapening' of the 3M scrubbies over the past year... thinner strands that break apart more quickly. The large ones from SAMS club are heavier strands/coarser density, but do not work as well as the smaller/ finer gauge that I get at Home Depot.
I always use 2 scrubbies meshed together.
I use the 0000 steel wool for polishing other metals....
When folks state STEEL WOOL, there are many,many grades, from very coarse to very fine....
If I used 0000 for wet scrubbing, I expect that somewhere down the road my drains will clog up with debris.... from the steel wool... :)