Your friend should tape the tub securely. Depending on the terminal, your friend may not be able to touch the tub after the TSA screens it. They have the supplies and should re-tape it if they need access to the contents.

Now, if your friend is wrapping the gifts and putting them in the tubs that may be a waste of time, if TSA needs to look at the gifts in the boxes. TSA would need to unwrap the boxes within the tubs anyway.