Hiding the dollar amounts from the contractor might not be worthwhile unless you were paid for the entire claim upfront. Insurance companies reimburse “recoverable depreciation” based on your actual incurred expenses. This means that any amount you save from the contractor just ends up staying in the insurance company’s pocket. Of course, if you are paid the full amount upfront, this doesn’t apply.
Example: Insurance estimates $20k damage, $5k recoverable depreciation, $1k deductible. You get a check for $14k. If your contractor says they will do the work for $15k, you don’t get any more money from the insurance company and the insurance company gets to keep that $5k.
Note that the insurance company’s estimate is usually fair when it comes to the dollar amount for the scope of work. One minor exception to this is when an estimate is generated very soon after a large storm event. In that case, the insurance company will usually update the estimate to a newer price list if you ask them to.