How can I clean the dirty tile pieces?

There's a cleaning machine located on the Central Plains.

You also need to make your own cleaning solution.

Or distill it.

There's a still on the wheel site.

It needs two ingredients.

One is near the still.

The item will fit in the hole on the still.

Put one of the mechanical seeds (growing in a field with small metallic
mounds) in the hole.

One of the other astronauts found the other ingredient you need.

He/she even labeled it for you.

It's the powder in the refrigerator at the tent site.  It will appear later
in the game if it's not immediately available.

Put that in the other slot on the still.

Finally, turn the wheel to get the still running.

The cleaning fluid you made will be on the right side of the still.

Press the button to release some of the fluid from the still.