In the audio world when you have questionable analog audio capture, the first thing you chase down is your power supply and the cleanliness of the power it provides. A bad power supply will muck up the sound of even the best ADC's.
The first thing I would try in this is to introduce a bypass capacitor, a small one (47uF@16v or so electrolytic should be fine and are readily available) at first, to the supply side of the RpiB. This is the simplest and cheapest way to first see if the noise is really coming from the DC supply.
You would hook the Capacitor up in parallel with the RpiB board so that all positive leads are tied together, and respectively all negative leads are tied.
Doing this will either require you to have a small breakout board with a female microUSB input and USB A header after the capacitor (also easiest to swap out capacitors), or directly soldering the capacitor to the backside of the RpiB board to the traces closest to the microUSB power connector.
If this helps the issue but still doesn't get it down a magnitude, I would suggest localizing the bypass capacitor closer to the USB jack of the microphone- this should help you by attempting to sink some of the high frequency noise on the DC lines right before it enters the power traces for the ADC inside. For best results a full isolation of the power supply, one that is completely separate from the Rpi itself and properly smoothed/filtered, would be most ideal, but also comes at both a physical and monetary cost to implement and becomes a question of just how important is it to you to eliminate a 1KHz noise and lower your noise floor.
I can't say I've had problems like this on my Rpi2B since it's been on the step-down isolation power supply I built for it, but I do remember the analog audio had a 1KHz or so sawtooth wave (and a horrible noise floor) to its output before switching to my own supply from a standard 5V2A phone charger.
To give more of a background, to just how expensive something can get for the best quality audio power supply, I've seen an "on-line" double conversion power supply supplying power to a MSB DAC board with a 140 femtosecond clock mounted on it. It was part of a system called "The Beast" http://www.msbtech.com/products/serverComp.php?Page=dac5home