Don’t use had pads on porcelain tiles, you’ll trash them.
IF you could remove the marks by polishing them, use a cream based product, but it’s still likely to dull the surface, esp if they’re polished.
Go to Halfords and look in the paint detailing section for a product called Farecla G3.
It's kind of like T cut, will need a bit of elbow grease, but it "cuts" in a very slow and controlled manner. You'll know pretty quickly if you're going to get a result. Ideally use it with a sponge applicator.
This kind of thing:-
That's the most likely solution to your problem.
For those interested, this product will remove light scratching from the surface of man made quartz (but only light marks) but you'll need a mechanical polisher with a felt mop or lambs wool bonnet to get any sensible degree of finish. sub 2000 rpm target speed preferable sub 1000 rpm.