Does tardigrade eat mould?
Mould in buildings can be serious.  It is treated by removing and destroying (fire is good) the things the mould is growing on, and lots of cleaning.  

The mould grows on wet cellulosic material like fiber board, gypsum board, paper, or wood.  It can be prevented by fixing the leaks so stuff doesn't get wet, and more cleaning.  

You could pour bleach on the contaminated material, kill some of the mould, and what survived would grow back.  Neither chemicals, nor tartigrades are any help here.  Just more cleaning.   

Details:  http://www.cdc.gov/mold/stachy.htm