How do you stop someone from using your mailing address?

Every month or so, we get some mail addressed to this person that doesn’t live at our address. (And to the best of our knowledge, did not live here before us.)

If it were just some junk mail or even a bill, I probably wouldn’t think too much of it. However, it’s from an institution that does drug testing. Seems kind of shady to me.

Things I’ve already tried:
– Wrote a note (please notify sender that addressee does not live at this address) on the envelope and left it for my mail carrier. They take it back, but new ones keep showing up.
– I called the institution/sender and asked them to stop mailing it to our address. They said it was confidential and they could neither confirm not deny that anyone by that name does testing at their facility. Which is moot because I’m already holding the damn piece of mail in my hand. I’m not asking for them to confirm it. I’m asking them to stop mailing it to my address.

What else can I do about this?