Remodeling, according to Tufts School of Veterinary Medicine's Animal Behavior Clinic, is one of the top 10 reasons for your cat to start urinating around the house. I know this for a fact since there always seems to be some remodeling project going on in my house.
The noise, smells, dust, chemicals, and strangers can create excessive stress for your cat, as well as for you. You need to handle the situation in such a way that your cat is safe, calmer, and not adding to your own strain. What you need to do first is put your cat in a room as far away from the actual project as possible, with all your kitty's necessities (food, water, bedding, litter box, and toys). Having music playing that your cat likes can serve two purposes. One is that music can calm him/her. The other is that it helps mask the remodeling noise.
You have to make sure that no worker opens the door because your cat is sure to try to escape.
Source: http://www.kadjaran.info