You could probably use
Command Velcro strips or something similar on the tiles and set the towel on top if bunching up of the towel is a problem.
Not exact matches
Put an iPad or Android tablet in a case, attach
velcro or 3M
Command strips to that case, and stick it to your fridge.
I hung the first paddle on the wall with two
Command Strips (a
velcro - like sticker).
Attach sink caddies with
velcro command strips to your pantry wall for all of your little kitchen items (spices, drink mixes, taco seasoning, soup mix, restaurant condiment packs, etc.).