By providing your license and SS Card you provide all your identification info to that company.
ASK THEM TO PUT THEIR REQUEST and the reasoning for that request IN writing and address it to your P O BOX address.
If you are a licensed contractor just show them your driver's license or State ID to identify you as the person you say you are.
That's more than enough. Some companies do those tricks to take time or avoid paying you or someone accused for something in the company and they try to get more info about you.
Just show them an ID that shows who you are.
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