In relation to your problem, let’s note that the white rings left on your flooring are nothing more than residues from an improper cleaning of the grout used for the joints, that has not been completely removed from the surface of the tile.
To remove these residues we use a product from Faber Chimica, calledTile Cleaner to be used according to the instructions attached:
Extra cleaning and restoration of tiles with TILE CLEANER
To use the TILE CLEANER to restore tiling use a wax coating or epoxy grout powders only as follows. Produces 5sqm. For flooring sections of around 3-4 meters. For coating, spread the pure product onto the flooring and leave it to set for at least 15 minutes (20 minutes if still soft or not flat) for epoxy grout leave it for 25/30 minutes or so. Rub with a green or black rectangular (scotch brite) sponge, depending on the surface of the floor, placing it under a brush or attached to a trowel. Straight after finishing rubbing, clean with water if possible, or a rubber rake to remove the dirt, bringing the residue to your feet where it can be picked up with a rag. Proceed with the same technique for the rest of the flooring in small areas of 2-3sqm. Once the process is finished, clean all of the surface that has been treated with floor cleaner, as per standard maintenance. In the even that you can’t find the specific product in its area, consider that there are other companies that produce similar products like Fila - 3M Italia and others; you can ask for a product with the same features when purchasing.
In anticipation of finding out the results from our suggestion, we send our best regards.