Can I clean the pieces that come with Osmo Math Wizard and the Amazing Airships?

Yes, you can!

For the tiles:

All the tiles can be cleaned with a damp cloth. Make sure to dry them with some napkins or a dry cloth.

For the play mat:

If you accidentally spill liquids or water on the play mat, towel dry it carefully, thoroughly, and quickly to ensure no damage occurs. Pay special attention to the edges of the mat, which are more vulnerable to water damage.

Note that any kind of dry erase, wet erase, or other markers will permanently stain and ruin the mats.