New tile floor installation question

I have contracted with HD to tear up existing tile and install new tile. When workers got the old tile up we discovered the concrete floor was not level. Some areas were over 1 inch higher then others. Workers suggested two ways to fix the problem. 1. Knock off the high areas with air hammer and then float the effected floor. 2. Float much more of the floor and much deeper because of the high spots. I chose option one. Did I choose wisely? Total area to be lowered about 8 sq feet. Btw, what is the best way to clean up the dust. Wiping with a damp cloth just smears the stuff. Any ideas? Chuck B.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.