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...I have the dogs about 3 feet from the background and the lights on either side. I'm trying to create a BLACK background, not charcoal.
With no EXIF info I can't say for sure, but it may be that you're recording too much room light in addition to your strobes. It could also be spill and bounce from the strobes, since you're using large modifiers.
Two things to try are moving the subjects further from the background, and moving the lights closer to the subjects...or doing both. These accomplish the same thing: getting more fall-off of the light before it reaches the background.
If it's ambient light that's causing the BG to be over-lit, a faster shutter speed may help cut down the ambient without affecting the strobe, unless you're already at max sync speed for your camera.
As for whether or not you should have a black background, you may get too much subject/background merge considering the subject is also black. If you do go for a black BG you'll almost surely need to add rim lights from behind the dog to create separation.