Here's the response I got from Roger Vitko at Tunze USA. Posted with permission.
Justin,
The pumps can vary in noise and it is possible for a pump to suddenly change in noise, I have owned pumps that suddenly got noisy and a few weeks passed and they got quiet. From dissecting dead pumps, I find this noise is usually caused by debris, often hair or threads snared on the shaft or in some cases the impeller rubbing the housing, which on a new pump would be a defect. This pump is very simply, it is for all practical purposes a 9V DC motor like you might buy for a science project that is sealed in a housing and the shaft goes through a rubber seal and turns an impeller. The main things that you can check and do to reduce noise is avoid any hard surface contact, in the intended installation the pump is suspended by the cable and hose in a plastic bucket, noise is substantially worse when it is in contact with a very rigid material like a glass or acrylic tank. Also, make sure all air is purged from the pump, any time they are out of water, air will become trapped in the pump and may cause failure to prime or noise, the air can be purged by tipping it upside down while submerged. Also, avoid non factory tubing, if the tubing is the wrong size and inserted too far, it will rub on the impeller. The factory tubing generally requires effort to insert and 1/4” is sufficient. If the noise is a grinding noise that is loud even when the pump is suspended, and the hose is correct, this points to an impeller rubbing on the housing and a factory defect. I would never consider this pump “quiet” but, suspended, in a typical bucket, with the bucket inside a cabinet, it should not be that loud that it is an issue or much louder than the system in general, you will definitely hear it run though.
Roger
While I do find it helpful and really appreciate the customer service that Tunze offers, this doesn't help me much. Perhaps I should have returned the pump right away but I didn't and it works fine. I have noticed when it runs dry, it'll make a lot of noise for a while when the air works it's way through. I've messed around with that possibility and, in my case, it isn't the case.