If you get your claim money for damages to your house from the insurance company and find a contractor to do the work for less can you keep the extra money from the claim?

Yes, you can keep the extra money you saved by finding a contractor to do the work cheaper than what the insurance company estimated. The insurance company prepared an estimate of the damage. If you could not find a contractor to do the work for what the insurance company estimated, you could ask them for more money. If they chose to pay you for the damage before it was fixed, they cannot ask for it back if you got the work done cheaper.