OP wants to carry them in his hand baggage so TSA opening checked bags is not relavant.
Yes the bag will be screend but those x-ray and other machines are pretty clever at showing humans what's inside not only the bag but containers that are in the bag.
I'd advise the OP to just tell the TSA person at the belt when they are loading up the tray that they do have 3 tins in the bag. They may appreciate the heads up and might say '"OK just put them in a separate tray".