There ought to be some cleaning utensils somewhere.
Utility cabinet
There is the utility cabinet at the Elevator. Take the the mop, soap and the bucket.
Empty bucket
Yes, there is some water at the Tower. Use the bucket in the pool.
And then
Well, you go to the mosaic, apply the soap to the water and and then combine the mop to the bucket filled with soap water. Mop the mosaic. Quite clear!
