I wouldn't use brick cleaning acid, which is basically dilute hydrochloric acid. Yes, it cleans the iron, but also Yes, it leaves chloride ions in the surface of the iron, which are very difficult to get rid of and will promote future rusting. (Same effect as common salt, which is sodium chloride.)
Far better to use the traditional pickle of dilute sulphuric acid, (if you can still get it after all the recent acid attacks). It's used concentrated as a drain cleaner, and in car batteries. When diluting it, remember:
"For safety's sake do as you oughter,
And add the ACID to the WATER. "
as it gets very hot. If you add water to acid it can boil and splash hot, concentrated acid all over you.
George