not sure where to post this, but need advice please.

I'll try ot make this as short as I can.

last week I bought a new car and I feel like I got scammed. I got a pre approval letter from my personal bank, when it came down to numbers the salesman did a 180 and was a total asshole along with the finance manager. they made me sign a "back up contract" just incase my bank fell through, (they didn't even acknowledge my letter) anyways I agreed fair enough, shit happens. so they "put my social in wrong" and it showed discrepancies with the number and my address. which is weird because I've never had an issue. I corrected the number on the form before finalizing all the pw. they asked me for proof of residency and asked for a picture of my ss card. obviously I didn't have it on me so they said I could email or text it when I got home. now my bank already mailed the check but finance manager keeps bugging me asking for my social. when I asked what was the reason (since social was only needed for back up contract and my bank already sent them their check) he came back with those discrepancies that they can either rerun my credit or I can send the picture of my card. they did run my credit because its showing on my credit report? I don't understand. I dont feel comfortable sending them my social card. it was a horrible experience and they got so much information wrong. I dont trust them. do I have to provide the card? I'm in Arizona idk if that matters.