This is the Gunlach scraper..
Gundlach 100 mm Scraper

This has to be one of my most favourite tools. Do not confuse it with the £1.99 market stall equivalents
100 mm wide blade, 300 mm overall length
Heavy duty cast alloy head
Made in the USA
Perfect for scraping and shaving off bumpy plaster or cleaning the back of tiles with old adhesive on.
Use for stripping up old vinyl tiles and cushion flooring
Insert between tiles to lever them apart (inserting spacers) with ZERO risk of chipping
Great for removing factory wax from wall tiles etc
Quality high grip Silicon rubber handle. made in the USA
A must have tool..
Personaly i would clean the salts off with the above scraper and a stiff bristled scrubbing brush and a quick clean with above product mentioned by Tel.. then leave it... do not wet it anymore..the floor needs to dry and whilst it dries the salts will continue to rise to the surface.
Eventually the effloresence will cease.. then you can start to renovate the surface.